Beck was born in the Washington Heights section of Manhattan in New York City, the son of Mabel Lucille (née Blum), a teacher, and Irving Beck, a businessman. He briefly attended Yale University, but dropped out to pursue writing and art. He was an Abstract Expressionist painter in the 1940s, but his career turned upon meeting his future wife. In 1943, he met Judith Malina (born 1926) and quickly came to share her passion for theatre; they founded The Living Theatre in 1947.
Beck co-directed the Living Theatre until his death. The group's primary influence was Antonin Artaud, who espoused the Theatre of Cruelty, which was supposed to shock the audience out of complacency. This took different forms. In one example, from Jack Gelber's The Connection, a drama about drug addiction, actors playing junkies wandered the audience demanding money for a fix. The Living Theatre moved out of New York in 1964, after the Internal Revenue Service shut it down when Beck failed to pay $23,000 in back taxes. After a sensational trial, in which Beck and Malina represented themselves, they were found guilty by a jury.
Beck's philosophy of theatre carried over into his life. He once said, "We insisted on experimentation that was an image for a changing society. If one can experiment in theatre, one can experiment in life." He was indicted a dozen times on three continents for charges such as disorderly conduct, indecent exposure, possession of narcotics, and failing to participate in a civil defense drill.
Besides his theatre work, Beck published several volumes of poetry reflecting his anarchist beliefs, two non-fiction books: The Life of the Theatre and Theandric and had several film appearances, with small roles in Oedipus Rex (1967), Love and Anger (1969), The Cotton Club (1984), 9½ Weeks (1986), and his role in Poltergeist II: The Other Side (1986). Beck also appeared in an episodes of Miami Vice.
In 1970 Beck's work was denounced alongside Eugène Ionesco and Samuel Beckett by Nëndori, the literary monthly of Albania, for supposedly being "inundated by mysticism and pornography."
Beck and Malina were life partners in an open marriage, and Beck had a long-term relationship with Ilion Troya, a male actor in the company. Malina and Beck shared a lover in Lester Schwartz, a bisexual shipyard worker who was the third husband of Andy Warhol acolyte Dorothy Podber. Beck and Malina had "two offstage children", Garrick and Isha.
Beck was diagnosed with stomach cancer in late 1983, and died two years later on September 14, 1985, at Mount Sinai Hospital in New York City, aged 60. He was survived by his wife, their two children, Garrick and Isha, and a brother. He was interred at Cedar Park Cemetery, in Emerson, New Jersey.
In 2003, 18 years after his death, Beck was posthumously inducted into the American Theater Hall of Fame. Judith Malina was also inducted to the Hall of Fame that same year.