Assuming the arm was in a position you could get to? Yes. Given a little time and the inclination, you can completely destroy someone’s arm (or, really, just about any body part,) with your teeth. The difficult part isn’t biting chunks out of someone’s arm, it’s being willing to bite chunks out of someone’s arm.
Think of it this way; your teeth are there to remove meat from bone, and they’re actually pretty good at doing it. On top of that, humans are one of the worst kinds of bites to receive. We build up some really nasty bacterial colonies in our mouths, and applying them to an open wound is a recipe for infection. Our immune systems (usually) recognize and know how to handle our own colonies. But, those are unique to an individual, so if you’re bitten by someone else, there’s no immunity, and the results are very unpleasant.
The hard part here is actually being willing to chow down on someone else. There’s a lot of social and psychological conditioning telling you not to bite fellow human beings.
The thing is, that conditioning is there to protect you. Exposure to blood is a fantastic vector for all kinds of illnesses that are otherwise non-transmittable. Some forms of viral Hepatitis and HIV are the big ticket items here; but, given the choice, there are many reasons to never touch a random stranger’s blood, much less gargle it.
So, you need to be willing to actually push past your own self preservation instincts, which is much harder than it sounds.
You also need to be willing to commit to seriously injuring your opponent. That’s a much easier threshold to hit, but combining it with the ability to shuck self preservation to mangle your opponent creates a weird paradox.
There’s a strand of combat philosophy that advocates rapid brutal escalation. Literally, “the best defense is a good offense.” You can see elements of this in a lot of the armed self defense forms. The problem is, outside of very extreme circumstances, biting someone takes the defense part of that equation out at the knees. You’re not using rapid escalation to protect yourself from attack, because you’re exposing yourself to far more potential harm now.
Now, obviously, you can end up with characters that have no problem taking out someone else’s throat with their teeth. But, that’s a rather singular kind of brutality. I did talk about the combat applications of brutality awhile back. So, that might be worth reading, if you haven’t seen it.