Not exactly eye mutilation, but there's a scene where Teddy plucks a hair that's growing out of his eye. There's some blood afterward, and his eye is undamaged, but it might be difficult to watch if you're squeamish.
This one's a bit on the cusp, but I'm going to err on the side of caution and say yes. There's a scene where Teddy is performing oral sex on his girlfriend and it eventually becomes uncomfortable. She tells him it hurts and pushes him away. It doesn't seem that any damage is done, but nevertheless, it's an uncomfortable scene.
There are two moments where there is a gunshot that comes out of nowhere. First one is a little past the 40 minute mark, and the second is around 1:09:10.
Surprise gunshots around the 40 minute mark, and another around 1:09:10. There's a third towards the end of the movie (1:23:15) but that one is a little more telegraphed.
Dead sheep are seen around 9:38 (when Teddy is walking in a field) and again at 39:30 (when Teddy wanders off into the woods). A dead wolf is seen from a distance around 1:09:10.