Actually, I stand corrected. Did some research and found out that they actually have teeny tiny little teeth, kind of like piranhas. They use them to latch on and shred anything that they bite. Fins, prey, fingers, that sort of thing.
Yes, they do have tiny piranha-like teeth near the back of their mouths. I read somewhere that proportionally, bettas have more bite force than a Great White shark. I never looked the same way at my sweet little betta, I can tell you.