Some TMNT stuff was always meant for grownups.
In his early years, Baxter Stockman obtained several degrees in the electronic and engineering fields, but he was particularly interested in microelectronics and robotics. However, his achievements in these areas didn't get recognized as he wished.
In Volume 1 of Eastman and Laird's Teenage Mutant Ninja Turtles, Dr. Baxter Stockman is a knowledgeable but sociopathic 36-year-old African-American scientist off "in his own world" with no relation to the comics version of Oroku Saki, also known as the Shredder, who used his talents to achieve his own selfish nefarious schemes rather than to help mankind. His latest invention, the Mousers, were small robots designed allegedly to find and exterminate rats in New York City, thus solving the city's rat problem. He developed the Mousers with the help of his software engineer, April O'Neil. Around the time when Baxter completed his invention, mysterious bank robberies were being committed, with small tunnels leading into the vaults.
When Stockman's assistant, April O'Neil, questioned him, he led her into an underground factory where hundreds of Mousers were being made. Stockman revealed he was really using the Mousers to rob banks. He also planned on sabotaging the foundations of certain important buildings throughout the city and holding them for ransom not because of the money (he could use his invention to make millions legally), but because "it's FUN!!!". Once April discovered his true intentions, she tried to escape through an elevator, but Stockman sent the elevator to sewer level. Stockman wanted her dead and sent the Mousers to eliminate her so that she wouldn't jeopardize his scheme. The turtles saved her from the Mousers that Stockman had sent to kill April. Not knowing that she was saved by the turtles, he continued his plans, holding the city for ransom with the threat of destroying several city landmarks with his Mousers. With the help of April, the turtles then successfully infiltrated Stockman's lab and managed to stop the Mousers for good. Soon, Stockman is taken into custody by the police.
Later, he reappeared in Volume 2 of the comics as a major villain. Stockman would somehow escape from prison and break into the DARPA facility to wreak havoc. After taking out the guards, he would somehow use the technology from DARPA to implant his brain into the body of a huge killer robot, making him a cyborg who wanted revenge. As the robot, Stockman would bust out of DARPA, seek out and find April and inject her shoulder with something which was, at the time, unrevealed. The Turtles, Casey Jones, and Nobody soon battle it out with the Baxterbot, which would result in Baxter losing an arm and blacking out, before Raphael was captured by DARPA. Regaining consciousness, Baxter would discover his robot body was fixed and somehow regenerated an arm. The other three Turtles and Casey find the Baxterbot in the sewers, ready to electrocute them with live power lines. Leonardo would turn the tables and electrocute the Baxterbot instead. While the Turtles wondered how Stockman got the robot to work, they didn't know his brain was actually inside it. Or so it would seem. Assumed to be destroyed; only the glasses he had retrieved earlier remained.
In Volume 4 of the series, however, April would fall prey to nanobots inside her system, threatening to destroy her body. It was revealed that this was what Baxter injected her shoulder with all those years ago. It was also revealed that, unbeknownst to anyone else, Donatello had maintained a secret sewer room where he kept the remnants of Stockman's cyborg robot body with Stockman's brain still alive and mounted up against a wall. Though understanding Stockman was a sociopath who should never be free, Don would have long talks with the fellow scientist in appreciation of his brilliant mind.
As it turned out, Stockman was once hired by the Utroms, which at the time were staying incognito on Earth, to overhaul their computer systems. On this occasion, Stockman stole a laboratory sample containing a set of prototype nanobots from the Utroms. Don went to Stockman to plead for a way to save April, but the doctor wouldn't tell him. He also tried tolling Don into more scientific discussions as an attempt to stall the turtle for time. Don spent long hours trying every angle to extract information from him, only to be disgusted by Stockman's sheer depravity. Don finally came to the late conclusion that Baxter Stockman was irredeemably evil. Don told him to rot in hell as he unceremoniously executed what was left of Stockman's cyborg body. The Utroms, Donatello, and the turtles eventually found a way to save April from Stockman's nanobots without any of the condemned scientist's help.
Stockman's name was inspired by a particular type of paper upon which some comics were being printed around the time the first few issues of the TMNT were published. It was prized for its bright whiteness and quality feel... and its name was "Baxter Stock".