Walsh was born in Ogdensburg, New York, the son of Agnes Katharine (née Sullivan) and Harry Maurice Walsh, Sr., a customs agent. He is of Irish descent. He was raised in rural Swanton, Vermont, and attended college at Clarkson University. He graduated in 1958 (B.A., Business Administration). In 1998, the Clarkson Alumni Association presented him with the Golden Knight Award.
In comedy, Walsh played the cynical small town sportswriter Dickie Dunn in the iconic 1977 hockey film Slap Shot, and a college diving coach in the Rodney Dangerfield film Back to School. According to Roger Ebert's Stanton-Walsh Rule, "no movie featuring either Harry Dean Stanton or M. Emmet Walsh in a supporting role can be altogether bad". Ebert later conceded that this rule was broken by 1989's Dream a Little Dream (Stanton) and 1999's Wild Wild West (Walsh).
Walsh came to prominence in the 1978 crime film Straight Time, in which he played a parole officer. He also had a small but memorable role as a crazed sniper in the Steve Martin comedy The Jerk. One of his best-known roles was Captain Harry Bryant in Ridley Scott's cult film Blade Runner. His most acclaimed performance was arguably the double-crossing private detective in Blood Simple (1984), for which he won the 1986 Independent Spirit Award for Best Male Lead.
Walsh made occasional guest appearances on Home Improvement as Tim Taylor's father-in-law. In 1992, he appeared as a powerful U.S. Senator in David Winning's Killer Image. In Christmas with the Kranks, he played one of the Kranks' neighbors. He also appeared as Alex Lembeck, a motorcycle cop who appointed himself as Sandy Stockton's chaperone and protector on The Sandy Duncan Show in 1972. He appeared in an episode of the NBC drama series Gibbsville in 1976 and Little House on the Prairie in 1981.