Master Splinter’s backstory changes quite a bit based on what incarnation you happen to be digesting, especially if it’s intended for younger audiences. In the 1980s and 2012 cartoons, for example, we are told that martial arts master Hamato Yoshi is simply mutated by the Mutagen along with the four turtles.
However, in the original comic book run, things were far different and far darker than anything that’d be allowed in a Saturday morning cartoon. The circumstances of Splinter being Hamato Yoshi’s pet remain still the same, but Yoshi’s characterization differs tremendously. Here, he and his rival, a man named Oroku Nagi compete for the affections of a woman named Tang Shen. Shen ended up choosing Yoshi, which sent Nagi into a blind rage, and he mercilessly beat her. This, in turn, caused Yoshi to snap and beat Nagi to death with his bare hands!
His death not only prompts Yoshi and Shen to leave Japan but it causes Oroku Saki, Nagi’s brother, to seek revenge. After extensive training, Saki becomes known as The Shredder, leader of the Foot Clan, and tracks the couple down in New York City. He brutally murders them both, leaving a pre-mutation Splinter without a caretaker and forcing him to scurry through the streets of the city. While the first theatrical film was partially accurate to this version, no subsequent adaptation ever dared to adapt this darker backstory beat-for-beat.