Can PhD students turn down teaching assistantships?
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.