How animals eat the food having no teeth?

I don't know what the scientific term for it is, but their mouths (especially the edges of their mouths) are very, very sharp, like a bird's beak. When they bite, it really, really hurts, and can easily draw blood. They don't really chew their food; they just break it up into smaller pieces with their beak-like mouths, and swallow the smaller pieces whole.