Oosumi hails from Hyogo Prefecture and studied at the Tokyo University of Technology's School of Media Science before launching his career as the leader of a puppet theater in Kobe. That experience eventually connected him to Tokyo Movie Shinsha, one of Japan's earliest animation studios.

He's best known for his work on two major 1969 projects. The Moomin TV series, developed with animator Yasuo Ootsuka, became an instant hit—but not without controversy. Tove Jansson, the Finnish author behind the original books, was deeply unhappy with how the characters were being portrayed, famously objecting that her Moomin was meant to have "No car, No fight, and No money." The series lasted just 26 episodes before moving to a different studio.

Around the same time, Oosumi and Ootsuka worked together on Lupin III, which didn't fare as well. The show struggled with poor ratings and was axed after 23 episodes, though it's now considered a classic. Oosumi directed the first seven episodes plus episodes nine and twelve; Hayao Miyazaki and Isao Takahata handled the rest. The experience soured things between Oosumi and the studio—he was let go for refusing to dumb down the sophisticated material for younger viewers.

After that rocky start, he went on to direct animation for various studios and NHK over the following decades. He made a brief return to the Lupin franchise in 1993 with an episode called "Orders to Assassinate Lupin."