Not in the actual show, but if I recall correctly there's a scene in the riffed "childrens" movie Merlin's Shop of Mystical Wonders where a dog burns to death.
The riffed short Catching Trouble is infamous in its portrayal of a man taking a bobcat, bear cubs, and rattlesnakes from the wild in a rather horrific fashion, doing things like chopping down trees they ran up and throwing them in bags. The bear cubs do some heartbreaking screams. Viewer discretion for that one is advised. The movie Cry Wilderness has a very uncomfortable scene where the villain chokes a baby raccoon, seemingly for real. While not pointed out by the riffers, I noticed that Carnival Magic has some very drugged looking tigers that pant in the heat and seem terrified of the actors.