Q:

Is the word 'remind' is stative verb? (remind vs. reminding)

Is the word remind a stative verb? (which means that even if I'm talking about something that's happening right now, I still have to use this infinitive verb without turning it into present continuous tense and addition of -ing)
For example:
If I am speaking right now with someone and he's saying to me something that causes me an association with something else, I have two basic choices to respond: 

a) You remind me (at the moment) of a quite similar anecdote that I came across two weeks ago.

or

b) You are reminding me of a quite similar anecdote that I came across
  two weeks ago.

A:

Both are correct, and identical in meaning.
As a response to something another person has just said, it is more common, especially in American conversational English, to use "that" as the subject, rather than "you": 
That reminds me of a similar anecdote that I came across two weeks ago.

But the two sentences in the question are correct and you would not sound strange or be misunderstood by anyone.
Finally, to actually answer your question, "to remind" is not stative.  It indicates an action, and not a state of being.  The corresponding stative construction would be:
I am reminded of a similar anecdote....

and notice this is a little bit different because nothing mentioned is /doing the reminding/.

