This is Splinter's original origin (from the first comic book)
Splinter was a simple pet rat to a ninja master by the name of Hamato Yoshi. He mimicked his master's movements from his cage. Yoshi was in love with a woman (fogot her name >< ). There was also another character - Oroku Saki (who would soon become the Shredder) was also in love with the woman, but she only loved Yoshi. Soon the two fled the their town and Japan, settling down for afew years in New York. Saki was plotting his revenge and managed to track the couple down. He killed the woman he once loved and then waited for Yoshi to come home. When he did, he was killed by Saki. In the process, Splinter's cage was knocked about and he was free and was somehow flung outside the window, that his life would never be the same again
And then comes in the part of the mutation and (of coarse) the Turtles
Insanity triumps over sanity...Mådness over reality...
The origin plot of the movie is also the origin plot of the comics.
The 80's cartoon changed a few things. Instead of Splinter being a pet rat, he was actually Homato Yoshi.
Yoshi was a master of the foot clan, Shredder wanted it, so he framed Yoshi for murder. Disgraced, Yoshi flet to America, where he was poor and forced to live in the sewers. Around that same time, a kid dropped his pet turtles down the drain and Yoshi found them.
Then one day, the mutagen was also flushed into the sewers. The mutagen was different in the older cartoon. Instead of making things simply bigger, it mutated things according to whatever animal they had most recently been in contact with. The turtles, because they hung around Yoshi a lot, turned human. Yoshi turned into a rat because he had mostly been in contact with rats.
Shredder mutated Bebop and Rocksteady by getting a pair of punks and exposing them to a Warthog and a Rhino along with the mutagen.
I personally think this explanation was far better. Yoshi WAS Splinter. It made the fights way more interesting between Shredder and Splinter.
Originally Splinter was Yoshi's ninja kicking pet rat. I always thought that was stupid. I much prefer the way the old cartoon redesigned it and made it a bit more more morbid and believable (sure the whole idea is far fetched, but at least the old cartoon stuck to its genetic alteration sci-fi feel as opposed to having a ninja kicking tiny rat in a cage which isn't believable even in sci-fi). It's part of the reason why I don't find the new series particularly exciting.