Origin

The "origin of the TMNT" refers to a series of events present in most TMNT fictional universes, which ultimately culminate in the mutations of Splinter and the Ninja Turtles. Most versions are similar to outline of Splinter's tale in the first issue of the Mirage comics. Hamato Yoshi is slain by Oroku Saki and Splinter takes refuge in the sewers, where he discovers four baby turtles have been dropped by a young boy. One day Splinter returns to find the turtles crawling in a strange ooze, and their mutations into humanoid creatures begins.

Though most versions of the origin include these similar elements, many differences are present. Some delve deeper into the past, some have added minute details, and some have even altered the origins of the ooze or the identities of the characters. The most well known versions are those presented in the 1990 film and the 1987 cartoon series, although they are wholly irreconcilable with one another.

Mirage Comics
The Mirage version of the origin story lays out what would become the most common elements among the origin stories. It is recounted to the Turtles after their first successful battle.

Decades ago in Japan, there existed a ninja clan known as the Foot. Among the Foot's ranks was Hamato Yoshi, Splinter's original owner. From his cage, Splinter enjoyed mimicking Yoshi's movements, forming the basis for his knowledge of ninjustsu. Hamato Yoshi often clashed with a fellow member of the clan, Oroku Nagi, over the love of a woman named Tang Shen. When it became clear that Tang Shen loved only Yoshi, Nagi arrived at her home and savagely beat her. She was saved by Yoshi, who in a moment of rage, killed Nagi with his bare hands.

Knowing that the Foot Clan would not accept the murder of another member, Yoshi, Tang Shen and Splinter fled to New York City, where he founded a small martial arts school. Meanwhile, the Foot continued to train Nagi's younger brother, Oroku Saki. Fueled by a thirst for vengeance, Saki eventually became a high ranking member of the organization, and was tasked with leading a branch of the Foot in New York. Once there, Saki adopted the mantel of the Shredder and lead the clan to the highest ranks of the underworld, specializing in burglary, espionage, and assasination. Yet the entire time, Saki sought the opportunity to avenge his brother by slaying Hamato Yoshi.

One night Yoshi returned home to find his appartment ransacked, Tang Shen lying dead on the floor. Yoshi then saw the Shredder, who, revealing his identity as Oroku Saki, promptly killed Yoshi with his blades. Alone and heartbroken, Splinter escaped into the sewers, rummaging for food to survive.

In 1969, a young boy was carrying four baby turtles home from the pet shop. A blind man was crossing the road when a truck labeled "T.C.R.I." almost ran him down. A young man behind the boy with the Turtles ran out to save the blind man, bumping the boy with the turtles and knocking the jar from his hands. The jar broke when it landed in the gutter, and the Turtles were washed down a sewer drainage grate. As the truck swerved, the back doors flew open. A container of green radioactive goo fell out and was subsequently washed down the drain with the baby turtles. The turtles landed safely, until the jar of goo fell beside them, coating them with its contents.

Moments later, Splinter came across the babies, gathering them into a can. He didn't realize he was coating himself with the green goo as he gathered them up. In very little time, Splinter and the turtles evolved and mutated into anthropomorphic beings with intelligence and emotion rivaling that of a human. Their mutation near completion, and educated, the rat named the Turtles after Renaissance artists - Leonardo, Donatello, Michelangelo, Raphael. For the next fifteen years, Splinter raised and instructed the young turtles, his sons, in the martial arts in order avenge his master.

It is later revealed that the ooze was created by a group of benevolent aliens known as Utroms.

This origin is shared with the Image continuity and the Palladium source books.

1987 Series
The 1987 series deviates noticably from the Mirage origin, completely removing Tang Shen and Oroku Nagi, and actually turning Hamato Yoshi into Splinter. In the series, Splinter relates his origin not to the Turtles, but to reporter April O'Neil.

As in all versions, Hamato Yoshi and Oroku Saki were members of the Foot Clan in 1960s Japan. Here the Foot Clan is portrayed as a peaceful organization, Yoshi himself a quite man who loved Renaissance art. He had a long standing rivalry with Oroku Saki, who always planned to overthrow Yoshi as leader of the clan. When a master sensei arrived, Saki planted a dagger in Yoshi's dogi (fighting outfit), framing him in an assassination attempt. Dishonored, Yoshi was excommunicated by the Foot and fled to New York, where he lived homeless in the sewers.

In Japan, Saki turned the Foot into an army of crime, using their ninja skills for personal gain.

Far later in New York, a boy dropped a fishbowl of baby turtles down a storm drain. Yoshi found them and raised them as pets. One day he discovered the turtles crawling in a broken canister of glowing, purple ooze, and proceeded to clean them. Yoshi later realized that the ooze was a powerful mutagen, capable of turning any lifeform into the animal it last touched. As the turtles had last touched Yoshi, they became humanoid. Yoshi, however, had most recently been in contact with the rats, and thus became a half-man, half-rat mutant.

As ever, Yoshi named his sons after Renaissance artists and taught them ninjustsu, although in the cartoon it was for protection rather than vengeance. Seeing his capacity to break boards, the Turtles began to call their master Splinter, a name which he willingly adopted.

The alterations in this origin story were likely due censorship placed on death within children's cartoons. It also served to introduce the gimmick of the cartoon's mutagen; its property to merge animal and human DNA was unique to the series and was used extensively in the origin stories for various mutants in the toyline. Whereas most versions depict the mutagen as a product of T.C.R.I., here it is created by Krang, who allowed Saki to dump it in the sewers in hopes of killing Hamato Yoshi.

This origin is shared with the comic series Teenage Mutant Ninja Turtles Adventures, where it is again recounted to April.

Movies
The origin in the movie continuity is largely similar to the Mirage version. It does, however, contain some minor differences. The character of Oroku Nagi is removed completely. Instead, Oroku Saki quarrels with Hamato Yoshi over the love of Tang Shen. Seeking to avoid conflict, Yoshi, Tang Shen, and Splinter flee to New York. However, they are followed by Oroku Saki, who kills them both in their home. Splinter leaps from his cage and permanently scars Saki's face. In retaliation, Saki slices off a portion of Splinter's ear, but allows the rat to escape.

From there on the story remains primarily unchanged. Splinter discovers four baby turtles crawling in a puddle of ooze in the sewer. Their mutations begin and Splinter teaches them martial arts for protection.

Of note is that the ooze here is not a product of TCRI, but the similarly named TGRI. The company is revealed to be a normal scientific firm, rather than an alien front like its comic book counterpart.

While it is never explicitly stated, it is likely that this origin is shared by the live action televsion series Ninja Turtles: The Next Mutation. The series never reveals a proper origin story, but certain visiual cues, such as Splinter's damaged ear, seem to imply similar events to those of the movies.