Cragun was born in Sacramento (California), United States. He studied at the Banff School of Fine Arts in Canada, the Royal Ballet School and Vera Volkova in Copenhagen. His artistic development is closely associated with John Cranko connected and engaged him in 1962 for Stuttgart Ballet. In Cranko's choreography - for example Romeo and Juliet, Onegin, The Taming of the Shrew - he became world famous. Even after Cranko's death he remained the Stuttgart Ballet to end his dancing career in 1996 faithful. There, and in his many guest appearances around the world, he worked with several choreographers who have significantly influenced the development of dance. He danced in choreographers by Kenneth MacMillan, John Neumeier, Jiri Kylian, William Forsythe and Maurice Bejart.

From 1996 to 1999 he was ballet director at the Deutsche Oper Berlin. He left Berlin in 1999 to start a new ballet company in the Brazilian city of Curitiba and at the Teatro Municipal of Rio de Janeiro together with his partner Roberto de Oliveira. Cragun was also a noted cartoonist, who mounted several exhibitions of his work.