Gordon was born in Boston, Massachusetts. He was mentored by Oscar Hammerstein, and appeared on Broadway in several musicals, including the original production of Oklahoma! (1943), Show Boat and Brigadoon. He also appeared in America's first television soap opera Fashion Story. He was named in a newsletter Red Networks that specialised in naming alleged communists and sympathisers, and after he refused in 1951 to sign a loyalty oath declaring that he was not a communist, work dried up completely.
He went to Sydney, Australia in 1949 to star in the musical Kiss Me, Kate. He stayed in the country and established the Ensemble Theatre in North Sydney with a group of young students he tutored from the Independent Theatre. This was a co-operative style theatre and also Australia's first theatre-in-the-round. He also established Australia's longest surviving acting school, the Ensemble Studios, in the 1950s, which closed in 2009. He was Principal of the school for the rest of his life. Toward the end of his life he published Acting and Performing which outlined his Stanislavsky-influenced acting methods. He passed on directorship of The Ensemble Theatre to Sandra Bates in 1986.
Hayes was a great friend and mentor to Australian actress Denise Roberts who taught film and television at the Ensemble Studios for Hayes for over 6 years. In September 2000, Denise established Screenwise and began teaching the Hayes Gordon philosophy for screen acting.
He had one daughter, Kati, who lived with her mother in the USA. He remarried in the early 1980s to Helen Terry and remained with her until his death.
He was appointed an Officer of the Order of the British Empire (OBE) in 1979, and an Officer of the Order of Australia (AO) in 1997, for his contribution to the arts.
He died in Sydney of heart disease.