Clohessy was born in the Bronx, New York, the son of John Clohessy, a police officer. He graduated from SUNY Purchase. He fought in the 1975 Golden Gloves in Madison Square Garden. He graduated from Pearl River High School in Pearl River, New York, and from SUNY Purchase.
He later joined the cast of the HBO prison drama Oz as Correctional Officer Sean Murphy. However, in between these roles, Clohessy had a supporting role as Thomas Smaraldo on NBC's comedy/drama Tattingers (1988–89), and soon after appeared in a starring role on NBC's short-lived comedy One of the Boys (1989). Clohessy co-starred on the Neal Marlens/Carol Black ABC sitcom Laurie Hill in 1992, playing a stay-at-home freelance Writer. In 2008, Clohessy had a regular role in the short-lived Fox show New Amsterdam. He won a Screen Actors Guild Award for Best Ensemble in the HBO series Boardwalk Empire.
In feature films, Clohessy played a supporting role in Across the Universe, playing the part of Jude's long-lost father. He played Jack Parker in The Crimson Mask. His largest big budget film role was opposite Ryan Gosling in The Place Beyond the Pines. Onstage, he played Mike in the Broadway Roundabout Theatre Company revival of Pal Joey, from November, 2008 through February 2009. In 2012 he had a cameo in the film The Avengers.
