Born in Akron, Ohio, Crawford majored in drama at Smith College. Following graduation, she moved to New York City and enrolled at the Theatre Guild. After performing in two productions, Juarez and Maximilian (1926) and The Brothers Karamazov (1927), she abandoned her acting career.
In 1931, Crawford created The Group Theatre with Harold Clurman and Lee Strasberg and began to direct. Her third effort, Men in White (1933), was the group's first commercial success and won the Pulitzer Prize for Drama. After directing two more productions, she decided to commit herself to producing and resigned from the company. As she recalled in her autobiography, "I felt exhilarated, even cocky, to be on my own. I was going to do great things, bring to audiences distinguished plays, quality entertainment." Her first major success was Golden Boy in 1937.
Crawford was influential in the early careers of such actors as Helen Hayes, Bojangles Robinson, Mary Martin, Ethel Barrymore, Ingrid Bergman, Tallulah Bankhead, and Paul Robeson, among many others. In 1946, she and Eva Le Gallienne founded the American Repertory Theatre. In 1947, together with Elia Kazan and Robert Lewis, she created The Actor's Studio, which trained Marlon Brando, James Dean, Jerome Robbins, Shelley Winters, Jane Fonda, Bea Arthur, and many more. Former partner Strasberg joined them as artistic director in 1951.