Born in New Jersey in 1957, Minion briefly attended NYU Film School before finishing his studies at Columbia University for screenwriting.

In 1984, Minion's script for After Hours was optioned by Griffin Dunne and Amy Robinson.

Robinson sent Minion's screenplay to Scorsese, whose Last Temptation of Christ had recently fallen through; production on After Hours started shortly afterward.

As a director, Minion made his debut for producer Roger Corman with 1987's Daddy's Boys.

Throughout his career he has taught film and screenwriting at School of Visual Arts, USC, The North Carolina School of Arts, Long Island University and the New York University School of Continuing Education.