You can say "Don't try to ___" when someone is acting badly and you're not going to allow it. For example, you can say this when your roommate takes some of your food but pretends that he didn't know that it was yours:
Don't try to play dumb. That wasn't an accident. You did it on purpose!
Or imagine that you're a parent and your teenage son is begging you to buy him a new video game system. You've said no, but he keeps begging you so you say this:
Don't try to debate me on this. My decision is final.