The powerful jaws of the alligator snapping turtle are effective at tearing flesh because they are covered in a sharp-edged horny beak.
“An alligator snapping turtle lies in wait for a passing fish, well camouflaged against the muddy river bed. Like all turtles and tortoises, it has no teeth, but its jaws are covered in a sharp-edged horny beak suitable for shearing flesh. On the floor of its mouth is a fleshy pink worm-like lure, which the turtle waggles to attract fish. Eager to seize the ‘worm’, a fish may swim right in the turtle’s gaping mouth.” (Foy and Oxford Scientific Films 1982:142)