He studied at Palo Alto High School and graduated from California Institute of the Arts in the early 1980s in the Character Animation department.
While he was working his way through CalArts, he was hired by Walt Disney Animation Studios in 1983 as an in-between artist foreign He was then a supervising animator for, before being a character designer foreign He also wrote the song "Good Company" for Oliver & Company (1988), before becoming a character animator foreign
He then became a director for two Roger Rabbit shorts called and and a pre-production script development for Beauty and the Beast (1991).
He also directed a Mickey Mouse short, which was only shown at Disney-Metro-Goldwyn-Mayer Studios called Mickey"s Audition (1992). Minkoff got his big break when he directed the Walt Disney Animation Studios feature film alongside Roger Allers.
Since then, he also directed, which were a mix of live action and computer animation, and then some fully live action movies like, and He directed DreamWorks Animation"s computer-animated film Mr.
Peabody & Sherman. He is also attached to direct the fantasy action adventure Chinese Odyssey.
As of 2014, he is producing Blazing Samurai, an animated family film inspired by Blazing Saddles and scheduled for a 2017 release.
He also participates as a member of the jury for the NYICFF, a local New York City Film Festival dedicated to screening films for children between the ages of 3 and 18.