user8157: I have noticed subtle thoughts (sankharas) can spontaneously pop up but mindfulness can quickly cut off & end those subtle thoughts so craving does not arise in relation to those thoughts. 
I have also noticed the mind via subtle craving can be drawn with some attraction towards an external sense object but mindfulness can quickly cut off & stop any attachment & becoming arising towards the sense object. 
Are there any Pali suttas that say the sankhara (2nd condition) and the craving (8th condition) referred to in Dependent Origination can arise without the further arising of attachment (9th condition), becoming (10th condition), birth (11th condition) and aging & death (12th condition)? 
Must every arising of ignorance, sankhara & tanha (craving) result in the Dependent Co-Arising of all twelve conditions of Dependent Origination? 

user43: Since you're looking for sutta quotes, here's some. I know you're not a fan of Visuddhimagga but there's one quote from that too (I'm sure I've seen this story in the Canon though - but can't find it, so quoting VM).
About "mindfulness can quickly cut off and end those thoughts", see e.g. MN101 Devadaha Sutta:

"Suppose that a man is in love with a woman, his mind ensnared with fierce desire, fierce passion. He sees her standing with another man, chatting, joking, & laughing. What do you think, monks: As he sees her standing with another man, chatting, joking, & laughing, would sorrow, lamentation, pain, distress, & despair arise in him?"
"Yes, lord. Why is that? Because he is in love with her, his mind ensnared with fierce desire, fierce passion..."
"Now suppose the thought were to occur to him, 'I am in love with this woman, my mind ensnared with fierce desire, fierce passion. When I see her standing with another man, chatting, joking, & laughing, then sorrow, lamentation, pain, distress, & despair arise within me. Why don't I abandon my desire & passion for that woman?' So he abandons his desire & passion for that woman, and afterwards sees her standing with another man, chatting, joking, & laughing. What do you think, monks: As he sees her standing with another man, chatting, joking, & laughing, would sorrow, lamentation, pain, distress, & despair arise in him?"
"No, lord. Why is that? He is dispassionate toward that woman..."
"In the same way, the monk, when not loaded down, does not load himself down with pain, nor does he reject pleasure that accords with the Dhamma, although he is not infatuated with that pleasure. He discerns that:   

'When I exert a fabrication (or "apply an antidote" - AV) against this cause of stress, then from the fabrication of exertion there is dispassion. 
When I look on with equanimity at that cause of stress, then from the development of equanimity there is dispassion.'

-- So he exerts a fabrication against the cause of stress where there comes dispassion from the fabrication of exertion, and develops equanimity with regard to the cause of stress where there comes dispassion from the development of equanimity. Thus the stress coming from the cause of stress for which there is dispassion through the fabrication of exertion is exhausted & the stress resulting from the cause of stress for which there is dispassion through the development of equanimity is exhausted.

Regarding perception of something desirable and perhaps even momentary impulse of tanha arising but not developing into upadana, I remember this story (this version is from Visuddhimagga not from Pali Canon) translated by Piya Tan:

This is like the case of the elder Mahā Tissa, a resident of Mt Cetiya. It is said that the elder Mahā Tissa was on his way from Mt Cetiya to Anurādhapura for his almsround. Now a certain daughter-in-law of family who had quarrelled with her husband, had set out early from Anurādhapura, all dressed up and decked like a heavenly nymph heading for a relatives’
  house. She saw a monk on the road, and being of perverse mind, laughed loudly.  
The elder, thinking, "What is that?" looked up, and seeing the bones of her teeth, attained to the perception of foulness, and so gained arhathood. Thus it was said:

Seeing the bones that were her teeth, he recollected it as his foremost perception.
    Standing right there, the elder attained arhathood.  

Now her husband, going along the road after her, seeing the elder, asked: "Bhante, have you seen a woman?” The elder said:  

Whether it was a man or a woman that went by I know not,
    But only that on this highway there went a pile of bones!"  


Which is sort of explained in AN 3.68:

'But what, friends, is the reason, what the cause, why unarisen passion does not arise, or arisen passion is abandoned?' 'The theme (sign, nimitta - AV) of the unattractive' it should be said. 'For one who attends appropriately to the theme (sign) of the unattractive, unarisen passion does not arise and arisen passion is abandoned...'
'But what, friends, is the reason, what the cause, why unarisen aversion does not arise, or arisen aversion is abandoned?' 'Good will as an awareness-release,' it should be said. 'For one who attends appropriately to good will as an awareness-release, unarisen aversion does not arise and arisen aversion is abandoned...'
'But what, friends, is the reason, what the cause, why unarisen delusion does not arise, or arisen delusion is abandoned?' 'Appropriate attention,' it should be said. 'For one who attends appropriately, unarisen delusion does not arise and arisen delusion is abandoned. This is the reason, this the cause, why unarisen delusion does not arise and arisen delusion is abandoned.'"

The point of all this is that on beginning stages, we have to use effort to stop the process of unfolding of dukkha, but on advanced stages dukkha is prevented through a fundamental permanent change in perception/interpretation.

8157: <p>I have noticed subtle thoughts (sankharas) can spontaneously pop up but mindfulness can quickly cut off &amp; end those subtle thoughts so craving does not arise in relation to those thoughts. </p>

<p>I have also noticed the mind via subtle craving can be drawn with some attraction towards an external sense object but mindfulness can quickly cut off &amp; stop any attachment &amp; becoming arising towards the sense object. </p>

<p>Are there any Pali suttas that say the sankhara (2nd condition) and the craving (8th condition) referred to in Dependent Origination can arise without the further arising of attachment (9th condition), becoming (10th condition), birth (11th condition) and aging &amp; death (12th condition)? </p>

<p>Must every arising of ignorance, sankhara &amp; tanha (craving) result in the Dependent Co-Arising of all twelve conditions of Dependent Origination? </p>
 43: <p>Since you're looking for sutta quotes, here's some. I know you're not a fan of Visuddhimagga but there's one quote from that too (I'm <em>sure</em> I've seen this story in the Canon though - but can't find it, so quoting VM).</p>

<p>About "mindfulness can quickly cut off and end those thoughts", see e.g. <a href="https://www.accesstoinsight.org/tipitaka/mn/mn.101.than.html" rel="nofollow noreferrer">MN101 Devadaha Sutta</a>:</p>

<blockquote>
  <p>"Suppose that a man is in love with a woman, his mind ensnared with fierce desire, fierce passion. He sees her standing with another man, chatting, joking, &amp; laughing. What do you think, monks: As he sees her standing with another man, chatting, joking, &amp; laughing, would sorrow, lamentation, pain, distress, &amp; despair arise in him?"</p>
  
  <p>"Yes, lord. Why is that? Because he is in love with her, his mind ensnared with fierce desire, fierce passion..."</p>
  
  <p>"Now suppose the thought were to occur to him, 'I am in love with this woman, my mind ensnared with fierce desire, fierce passion. When I see her standing with another man, chatting, joking, &amp; laughing, then sorrow, lamentation, pain, distress, &amp; despair arise within me. <strong>Why don't I abandon</strong> my desire &amp; passion for that woman?' So he abandons his desire &amp; passion for that woman, and afterwards sees her standing with another man, chatting, joking, &amp; laughing. What do you think, monks: As he sees her standing with another man, chatting, joking, &amp; laughing, would sorrow, lamentation, pain, distress, &amp; despair arise in him?"</p>
  
  <p>"No, lord. Why is that? He is dispassionate toward that woman..."</p>
  
  <p>"<strong>In the same way</strong>, the monk, when not loaded down, does not load himself down with pain, nor does he reject pleasure that accords with the Dhamma, although he is not infatuated with that pleasure. He discerns that:   </p>
  
  <ol>
  <li><strong>'When I exert a fabrication (or "apply an antidote" - AV) against this cause of stress, then from the fabrication of exertion there is dispassion.</strong>   </li>
  <li><strong>When I look on with equanimity at that cause of stress, then from the development of equanimity there is dispassion.'</strong></li>
  </ol>
  
  <p>-- So he exerts a fabrication against the cause of stress where there comes dispassion from the fabrication of exertion, and develops equanimity with regard to the cause of stress where there comes dispassion from the development of equanimity. Thus the stress coming from the cause of stress for which there is dispassion through the fabrication of exertion is exhausted &amp; the stress resulting from the cause of stress for which there is dispassion through the development of equanimity is exhausted.</p>
</blockquote>

<p>Regarding perception of something desirable and perhaps even momentary impulse of tanha arising but not developing into upadana, I remember this story (this version is from Visuddhimagga not from Pali Canon) <a href="http://www.themindingcentre.org/dharmafarer/wp-content/uploads/2009/12/19.14-Nimitta-anuvyanjana-piya.pdf" rel="nofollow noreferrer">translated by Piya Tan</a>:</p>

<blockquote>
  <p>This is like the case of the elder Mahā Tissa, a resident of Mt Cetiya. It is said that the elder Mahā Tissa was on his way from Mt Cetiya to Anurādhapura for his almsround. Now a certain daughter-in-law of family who had quarrelled with her husband, had set out early from Anurādhapura, <strong>all dressed up and decked like a heavenly nymph</strong> heading for a relatives’
  house. She saw a monk on the road, and <strong>being of perverse mind</strong>, laughed loudly.  </p>
  
  <p>The elder, thinking, "What is that?" <strong>looked up</strong>, and seeing the bones of her teeth, attained to the perception of foulness, and so gained arhathood. Thus it was said:</p>
  
  <blockquote>
    <p>Seeing the bones that were her teeth, he recollected it as his foremost perception.<br>
    Standing right there, the elder attained arhathood.  </p>
  </blockquote>
  
  <p>Now her husband, going along the road after her, seeing the elder, asked: "Bhante, have you seen a woman?” The elder said:  </p>
  
  <blockquote>
    <p>Whether it was a man or a woman that went by I know not,<br>
    But only that on this highway there went a pile of bones!"  </p>
  </blockquote>
</blockquote>

<p>Which is sort of explained in <a href="https://www.accesstoinsight.org/tipitaka/an/an03/an03.068.than.html" rel="nofollow noreferrer">AN 3.68</a>:</p>

<blockquote>
  <p>'But what, friends, is the reason, what the cause, why unarisen passion does not arise, or arisen passion is abandoned?' 'The theme (sign, nimitta - AV) of the unattractive' it should be said. 'For one who attends appropriately to the theme (sign) of the unattractive, unarisen passion does not arise and arisen passion is abandoned...'</p>
  
  <p>'But what, friends, is the reason, what the cause, why unarisen aversion does not arise, or arisen aversion is abandoned?' 'Good will as an awareness-release,' it should be said. 'For one who attends appropriately to good will as an awareness-release, unarisen aversion does not arise and arisen aversion is abandoned...'</p>
  
  <p>'But what, friends, is the reason, what the cause, why unarisen delusion does not arise, or arisen delusion is abandoned?' 'Appropriate attention,' it should be said. 'For one who attends appropriately, unarisen delusion does not arise and arisen delusion is abandoned. This is the reason, this the cause, why unarisen delusion does not arise and arisen delusion is abandoned.'"</p>
</blockquote>

<p>The point of all this is that on beginning stages, we have to use effort to stop the process of unfolding of dukkha, but on advanced stages dukkha is prevented through a fundamental permanent change in perception/interpretation.</p>
