Slasher is the olive-green sharptooth from Land Before Time V: The Mysterious Island. DarkHououmon named him Slasher so it would be easier for her to incorporate him into the fanfic Out of the Shadows.
The Mysterious Island
Not much is known about Slasher in the movie. He appears as a rogue sharptooth that somehow got onto the island before the landbridge broke. He comes across Littlefoot and the others and starts to hunt them down. Chomper tried to stop him, but failed. Chomper's parents, whom DarkHououmon named Goldclaw and Sly, rushed in and fought Slasher and were able to knock him over the edge.
Unfortunately this knocked over Chomper. Slasher tried to get at Chomper, but Littlefoot pulled Chomper into the still water while the powerful current pushed Slasher away. His fate is unknown.
Out of the Shadows
According to Out of the Shadows, Slasher is the reincarnation of another sharptooth who started a war against the plant-eaters. Slasher takes in Chomper after his parents died at the jaws of two megalodons. He then trains Chomper to become a bloodthirsty killer, something that is forbidden among the sharpteeth. Slasher later dies, and Chomper takes over.
Towards one point in Out of the Shadows, it is revealed that Slasher was never involved in this. It was really Gris in disguise. He had been playing the part of Slasher, and tricked Chomper so easily into turning against his plant-eater friends. The whereabouts of Slasher, and the notion if he's even still alive, is unknown.