Kupfer's career began in Stralsund, then part of communist East Germany, in 1958. After stations in Chemnitz — formerly Karl-Marx-Stadt — Weimar and Dresden, he became director at the Komische Oper in 1981, a position he held for 21 years.
Kupfer gained international attention with his 1978 production of “The Flying Dutchman” in Bayreuth. He worked closely with conductor Daniel Barenboim, first on the 1988 production of Wagner's ‘Ring’ cycle — also in Bayreuth — and on a wider selection of the German composer's works at the Berliner Staatsoper from 1992 onward.
Kupfer also directed performances in Sydney, Barcelona, Helsinki, Salzburg, Shanghai and New York. He returned to the Komische Oper a final time earlier this year, with Handel's "Poro."