Baxter Stockman is the owner of Stock Gen Laboratories, a genetic research lab. On the payroll of the mysterious General Krang, he has his scientists researching applications of a Mutagen for Krang's warriors, most of which involves animal testing and harvesting.
When he was a young lad, Baxter's father would aggressively taught him to play chess, to hone his skills and intelligence. This would come back to bite him, as Baxter used these tactics to take Stock Gen from him.
Some of the experiments involved increasing the intelligence of rats, and adapting Turtle plastrons as natural armor. Ninja had broken into the lab and scared Stock Gen's intern, April O'Neil, in an attempt to steal the Mutagen and some of the animals. As a result, during their escape, the Turtles and rat were exposed to the Mutagen (this is how he created Teenage Mutant Ninja Turtles and his master Splinter) as well as an alley cat..
Krang charged Stockman with retrieving the Mutagen from the rat Splinter's bloodstream. Baxter had recruited the mutated cat, Old Hob, to send his Mousers after Splinter, and although he was successful in capturing Splinter, he was then claimed by the Foot Ninja clan. Stockman instead extracted the Mutagen from Old Hob's DNA, and finding no more use for the feline, shot him dead. Afterward, Stockman was drugged to sleep by Krang's men to come with Krang.
Stockman woke up in Krang's headquarters on Burnow Island and entered a room with containers filled with Ultroms, Krang's kind. Stockman is then encountered by Krang, who revealed his true self to Stockman and that he came from the planet Ultrominon from Dimension X. Krang explained that Stockman was brought to Burnow Island because since Stockman's talent for building the Mousers was not a disappointment, Krang decided to hire Stockman to use his mechanical skills to finish Krang's war machine, the Technodrome.