Can PhD students turn down teaching assistantships? This question deals with PhD programs which guarantee their students funding via teaching assistantships in the US.

In order to have more time for themselves (e.g., for PhD research, or for working a higher-paying part-time job), are PhD students normally allowed to decline teaching assistantships, as long as they're willing to forgo the department's stipend?

In addition to losing the stipend, are there other disadvantages to declining a TA position? (E.g., would tuition no longer be free?, could the department be frustrated?, etc.)
Turning down a teaching assistant position in your position is probably a very poor idea.

The renumeration for working as a TA normally covers both the a stipend and your graduate tuition.  If you do not have some other form of support (research assistantship or fellowship), you will have to pay your own way entirely.  This is normally financially prohibitive, although there are sometimes exceptions.

Moreover, some doctoral programs (such as my own) actually require that students spend a certain time working as TAs.  The teaching is considered a part of their professional training.  So even students who might have other ways of funding their entire graduate education may have to spend a certain amount of time teaching.