Graff is an alumnus both as a camper and counselor of the Stagedoor Manor performing arts summer camp in upstate New York. He sang on the original-cast albums of Sesame Street (1970) and the follow-up Sesame Street 2 (1971). He garnered fame in 1975 when he joined the cast of the PBS children's television series The Electric Company. Playing the role of Jesse, a member of the Short Circus, he remained with the show to the end of its production in 1977 (replacing Stephen Gustafson).