He initially studied medicine at the Universities of Tübingen and Berlin, but moved into theatre during the 1950s, during which he worked at the Staatstheater Stuttgart as actor and assistant stage director.

He directed plays at the Vienna Burgtheater, the Schiller Theater in Berlin, the Residenztheater in Munich and the Salzburg Festival (Leonce and Lena, Nathan the Wise, La Folle Journée by Beaumarchais).

He directed opera at the Salzburg Festival: Capriccio, The Magic Flute and Die Entführung aus dem Serail, working with conductor Georg Solti.

At the Royal Opera House Covent Garden in London he directed Mozart's Idomeneo, The Marriage of Figaro (1987), Così fan tutte (1989), and Don Giovanni.

Schaaf lived and worked for many years of his early career with actress Rosemarie Fendel; since 1984 he is married to opera singer Stella Kleindienst [de].