does this ascender tear up rope? looks like the teeth may cut into the rope.

They're designed to just separate the fibers of the sheath without causing any permanent damage. Once Tension is applied to the rope again the previous splits are closed and the rope reverts to normal. That said, they will cause small snags occasionally, but nothing seriously damaging.

Michael, In my experience with this piece, the teeth have caused little/no noticeable damage to my rope beyond a little cosmetic damage to the sheath in the form of minor snags. These were usually in areas where the rope was already frayed, and were worst on my dynamic rope... avoid ascending on a dynamic line if at all possible. Happy trails! Happy trails!

No, they roll up the rope then dig in a little when pressure is applied. Petzl knows what they're doing with this stuff.