As a schoolboy Schütter had piano and organ lessons as well as theoretical instruction with Antoine Cherbuliez. After studies at the Zűrich Conservatoire, Schütter travelled in Switzerland and abroad as an accompanist, received a small Rome scholarship in 1939, and studied by correspondence with Willy Burkhard during the war and with Paul Hindemith at Zurich University from 1950 to 1954. He earned his living at the Zurich Opera as ballet repetiteur and director of lighting, at the same time being active as a composer. Since 1976 he has lived as a freelance composer in Küsnacht (Canton of Zurich).