DeMunn was born in Buffalo, New York, the son of Violet (née Paulus) and James DeMunn. He graduated from Union College with a Bachelor of Arts in English. He moved to England in the early 1970s, receiving theatrical training at the Old Vic Theatre. When he returned to the States, he performed in a Royal Shakespeare Company production of King Lear and several off-Broadway productions, including Bent, Modigliani and A Midsummer Night's Dream.
He is known as a favorite of director Frank Darabont, who has cast him in all four of his films, The Green Mile, The Shawshank Redemption, The Majestic and The Mist. He also has an extensive television resumé, appearing in shows such as Kojak, Law & Order, and two of its spin-offs, SVU and Trial by Jury.
He has been involved in more Stephen King adaptations than any other actor. As of 2008, he has acted in film adaptations of Rita Hayworth and Shawshank Redemption, The Green Mile, The Mist and the T.V. miniseries Storm of the Century. He also narrated the audiobooks for Dreamcatcher and The Colorado Kid.
In 1995, he won a CableACE Award as Best Supporting Actor in a Movie or Miniseries for his portrayal of serial killer Andrei Chikatilo in the HBO film Citizen X.