Spiner was born in Houston, Texas, the son of Sylvia, a corporate vice president, and Jack Spiner, who owned a furniture store. After Jack's death, he was adopted by Sylvia's second husband, Sol Mintz, whose surname he used between 1955 and 1975. Spiner attended Bellaire High School in Houston, Texas, where he was influenced by drama teacher Cecil Pickett – the same drama teacher who coached such people as Cindy Pickett, Randy Quaid, Dennis Quaid, Trey Wilson, Robert Wuhl, and Thomas Schlamme. Spiner would become active on the Bellaire Speech team; later, winning the national championship in dramatic interpretation. After attending the University of Houston and performing in local theatre there, Spiner moved to New York City, where he became a stage actor, performing in several Broadway and off-Broadway plays, including The Three Musketeers and Stephen Sondheim's Sunday in the Park with George. At the same time, he also had nonspeaking background in the film Stardust Memories as one of the silent Felliniesque "grotesques" on Sandy Bates's train car.