Azito was part of the Juilliard School's Group I, the first students admitted to the drama division directed by John Houseman in 1968.
His interest in dance aggravated Houseman, who was anxious about the number of gay men in Group I and had already clashed with Azito over a cross-dressing incident.
In 1971, he performed in The Red, White, and Black at La MaMa, directed by John Dillon and written by Eric Bentley with music by Brad Burg.
[14] Azito made his Broadway debut in Richard Foreman's 1976 revival of The Threepenny Opera for the New York Shakespeare Festival, in a dancing role ("Samuel") created especially for him.
Critics were intrigued by what soon became Azito's style of dance, which made him look like a somewhat off-kilter marionette and was accompanied by stylized facial expressions.
"[15] This production also began Azito's association with Joseph Papp's New York Shakespeare Festival, which continued with another Brecht-Weill musical, Happy End (1977).
Azito's best-known stage role was in a third production for the New York Shakespeare Festival, as the Sergeant of Police in the 1980 Broadway revival of The Pirates of Penzance, starring Linda Ronstadt and Kevin Kline.
He went on to perform at Radio City Music Hall, the Mark Taper Forum, and in the American National Theater company at the Kennedy Center.
He went on to perform in a summer stock revival of She Loves Me in Stockbridge, Massachusetts and in productions of Tom Stoppard's Travesties and the musical Amphigorey.