Alexander was born Jason Alexander in New York City, the only son of actress Jane Alexander and her first husband Robert, founder and former director of The Living Stage. After attending New York University, he began his professional career as the stage manager of a 1983 Broadway revival of The Caine Mutiny Court Martial, in which he also played a small role. He also appeared on stage in I'm Not Rappaport and the Stephen Sondheim musical Assassins, in which he portrayed Lee Harvey Oswald. His screen roles included Matewan, Eight Men Out, and Clueless.