Morton made his Broadway debut in Hair and was nominated for a Tony Award for Raisin.

He has appeared in over 70 movies including Terminator 2: Judgement Day (as Dr. Miles Bennett Dyson) and has made many notable TV guest appearances, including his appearances as Dr. Hamilton in the first and second seasons of Smallville. Morton has starred on the TV series Equal Justice (1990–91), Under One Roof (1995) and E-Ring (2005). He has made several appearances as a defense attorney on Law & Order. He has also directed and produced. In 2006, he portrayed the jack-of-all-trades scientist, Henry Deacon as a regular on Sci-Fi Channel's series Eureka.

On daytime, Morton has had roles on Search for Tomorrow (Dr. James Foster, 1973-74), Another World (Dr. Abel Marsh and Leo Mars, 1983-84), and All My Children (Dr. Zeke McMillan, 2002).

Morton was born in New York, New York to Evelyn, a secretary, and Joseph T. Morton, Sr., a U.S. army intelligence officer. Because of his father's profession, he spent parts of his childhood in West Germany and Okinawa. In October 1984, he married Nora Chavooshian. He has three children: daughters Hopi and Seta, and son Ara. He also has a grandson, Moses.