Hawkins majored in Greek civilization at Harvard University, graduating in 1930. But a performance by the German dancers Harald Kreutzber and Yvonne Georgi so impressed him that he went to Austria to study dance with the former. Later, he studied at the School of American Ballet. Soon he was dancing with George Balanchine's American Ballet. In 1937, he choreographed his first dance, Show Piece, which was performed by Ballet Caravan.
The next year, Hawkins was the first man to dance with the company of the famous modern dancer and choreographer Martha Graham. The following year, he officially joined her troupe, dancing male lead in a number of her works, including Appalachian Spring in 1944. The two were married in 1948. He left her troupe in 1951 to found his own, and they divorced in 1954.
Not long afterwards, he met and began collaborating with the experimental composer Lucia Dlugoszewski. They remained together for the rest of his life.