Minchin's background is in theatre and he has appeared in various stage productions. He played the title role in the 2006 Perth Theatre Company production of "Amadeus", a fictional play about the downfall of Mozart at the hands of the reigning court composer, a character based on and named after Antonio Salieri. His other stage acting roles have included the title role in the 2004 Perth Theatre Company / Hoopla production of "Hamlet", and The Writer in the original PTC production of Reg Cribb's "The Return". He has also acted for The Australian Shakespeare Company ("Twelfth Night"), the Black Swan Theatre Company ("Così", "One Destiny"), and in various other plays, short films, and television commercials. Roles from his days in musical theatre include Don Quixote in "Man of La Mancha" and Pontius Pilate (and understudying Judas Iscariot twice) in "Jesus Christ Superstar". He has also appeared playing small parts on the ABC telemovie "Loot" and on the show "Comedy Inc.".