Yoshi's story, explained in the first movie mirrors the story of the original comic books, except Oroku Nagi is removed from the story and the conflict is with Oroku Saki himself rather than Oroku Nagi. Instead of fleeing the clan because of a murder of a clan member, Tang Shen persuades Yoshi to flee to America in order to avoid dueling Saki, (presumably to the death) for her hand in marriage. Saki vows vengeance and spent years searching for them. Saki eventually finds and kills both Yoshi and Shen in their New York apartment, leaving Yoshi's pet rat Splinter homeless. The actor who portrayed him was uncredited.
In the third Teenage Mutant Ninja Turtles film, the turtles save a child named Yoshi from a burning building in 17th century Japan, Michaelangelo getting him out of the building and Leonardo subsequently performing CPR. This Yoshi's relationship with Hamato Yoshi is never fully explained, but based on the past incarnations of another character that the turtles meet on this adventure (such as a possible British ancestor of Casey Jones, Whit) a direct relationship between this boy and Hamato Yoshi seems implied. If this is indeed the case, then when the turtles save the boy's life, they are also saving their own future, as their origin is inexorably tied to the fate of Hamato Yoshi. If this were true, however, Yoshi would have to be taken as the character's family name instead of personal name, in this canon.