Blum started acting on stage in the 1970s. In the 1980s, he acted in these movies: Lovesick (1983), Desperately Seeking Susan (1985), Just Between Friends (1986), Crocodile Dundee (1986), Blind Date (1987), and The Presidio (1988).
On television, he co-starred in Sweet Surrender in 1987, and he appeared in Capital News in 1990. From 2014 to the present, he has appeared in Mozart in the Jungle and Coin Heist (2017).
He won an Obie Award for his performance as Al in the Playwrights Horizons production of Albert Innaurato's play, Gus and Al, in the 1988–1989 season. On Broadway, he appeared in Neil Simon's Lost In Yonkers, Gore Vidal's The Best Man, and Richard Greenberg's The Assembled Parties. In 2013, he appeared as Max in the Primary Stages production of The Model Apartment. Blum currently is on the faculty of HB Studio in New York City.
