Mirage Comic Version
In the original Mirage comics Yoshi was owner of a pet rat who would later be called Splinter. He was also a member of Japan's dealiest ninja clan the Foot. Within the clan he had a rival called Oroku Nagi with whome he competed in all things including trying to win the favor of the lady Tang Shen. Both tried to win her hand but from the beginning she loved only Yoshi. One day he walked into Shen's home to find her being beaten by Nagi who demanded that she love him and in a fit of pure rage Yoshi murdered his rival.
Unfortunately by killing a member of his own clan he had brought on shame, he was face with two options; take his own life and hope for honpr in the next or face exile from the clan. Yoshi chose the latter option and along with Shen and his pet rat started a new life in New York. Years later Nagi's younger brother Saki had come to the city to lead a New York branch of the Foot. Now calling himself the Shredder he siezed the opportunity to avenge his brother he went to Yoshi and Shen's home killing both of them in cold blood leaving only Yoshi's pet rat whos cage had been broken in the battle.
The rat lived on the streets until witnessing a road accident involving a truck carrying cannisters of toxic waste. Seeing an errant cannister strike a boy's glass bowl filled with four baby turtles and seeing both the cannister and the reptiles fall down an open manhole the rat decided to follow them into the sewers. Seeing the cannister broken and the turtles covered in the toxic goo the rat gathered the turtles up getting the goo on himself. The toxic waste had an unexpected affect of mutating them, giving them human-like features such as speach and the ability to walk upright. The rat whom the turtles called Splinter decided to raise the turtles and train them in the art of Ninjitsu so that one day they could track down and kill the Shredder, thus avenging the death of his own master.
Years later Splinter took the four turtles to Japan. He showed his sons the site that was Yoshi's house which had been burned down by the Foot for his betrayal, Splinter hoped that any members of Yoshi's family would have escaped before this happened. Later he took them to Shen's house they encountered the spirit of Nagi who had haunted it even since he was killed there. Rescueing two children that were playing in the house Splinter set fire to the house. Escaping from the house Splinter could not sense Nagi's spirit and believed it had been released from the house. As they walk away the sprits of Yoshi and Shen are shown to be at peace.
1987 Animated Version
In the popular 1987 Teenage Mutant Ninja Turtles cartoon Yoshi had a much more prominent role in that he became Splinter. His story once gain starts in Japan as a lover of art and member of a noble Foot clan with his rival this time being Oroku Saki who sought lead. When a master teacher visited the Foot school Saki framed Yoshi of conspiracy to murder the teacher which led to his banishment from the clan.
In disgrace Yoshi fled to New York, penniless he lived in Sewers with the rats as his only company until a boy accidently dropped his pet turtles down the drain. Yoshi lived peacefuly with his turtles and rats until one day he found the turtles covered in some kind of ooze. Cleaning the turtles and getting ooze on himself in the process he discovered that it was a powerful mutagen which caused whoever touched it to take on the form of whatever animal they'd most recently come in contact with. The turtles started to become more human because they'd most recently been with Yoshi, but Yoshi himself started to become a rat-like. The four young turtles nicknamed the rat Splinter and he in turn named them after his favorite renaisance painters. Knowing that the outside world would not understand them, Splinter trained the turtles in art of Ninjitsu. The turtles themseves vowed to one day track down whoever made the mutagen and force them to make their master human once more.
While helping a reporter named April O'Neil uncover the truth behind a wave of ninja robberies the turtles and Splinter discover that it was Oroku Saki who had dropped the mutagen in the sewer tunnels with the intention of destroying him. Now calling himself the Shredder, he had built the Foot into a high tech army of crime. The Shredder had in his possession a retromutagen ray generator, a device which undoes mutations. Knowing that this was the only device capable of turning Splinter back into Hamato Yoshi the turtles and Splinter were eager to get it. When the Shredder turned the device on the turtles however, Splinter destroyed the device in order to save his young friends. When Leonardo lamented Splinter's decision, the rat simply started that it was perhaps his karma to live his life as a rat.
Splinter would reverse to Hamato Yoshi once in the series. When Splinter began to pine for human life Donatello used a small portion of the mutagen that changed them all to revert their master to human form. Moved to tears Yoshi went out to experience human life once more leaving the turtles to wonder if Yoshi's regaining his life would mean he would permenantly leave them. Unfortunately Yoshi found his return to human life unfulfilling and when he unexpectedly started to revert to being a mutant rat he was hunted down by scared and angry humans. In the end Yoshi fled into the sewers and turned back into Splinter fully he was able to use his rat senses to track down the turtles and help them thwart Shredder's plan to open a portal to Dimension-X.
Archie Comic Version
The Archie comic version of the character was originaly identical to the 1987 cartoon version as the early issues of the comic adapted episodes of the cartoon but began to tell original stories. Later in the series it fleshed out much of Hamato Yoshi's backstory and even retconning parts of the established cartoon origin.
As a youth a young Yoshi would go to the mountains surrounding Hiroshima to train ninjitu with his Uncle Gyogi were they both witnessed fall of the atomic bomb in 1945. The sight of the blast blinded Gyogi and Yoshi and his family moved north to escape the nuclear fallout. Gyogi continued to train with Yoshi to try and relieve him the young man the anger he felt inside. After studying at Osaka University Yoshi enrolled in the Foot Clan and along his friend Oroku Saki became one of their fiercest warriors.
Yoshi left the Foot for a year traveling to the Crystal Palace in Tibet to study spirituality under Charlie Llama. Their he was purged of his anger and returned to lead the Foot. One his return Saki felt that Yoshi had grown soft and was no longer fit to lead. When the Master teacher visited the Foot Saki framed Yoshi for the murder of the teacher's aid thus he was banished from the clan.