After attending New York University, Alexander 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. Alexander appeared on stage in I'm Not Rappaport, Six Degrees of Separation and the Stephen Sondheim musical Assassins, in which he portrayed Lee Harvey Oswald. His screen roles include City of Hope, Love and a .45, Matewan, Eight Men Out, Crocodile Dundee II and Clueless.
In the early 1990s, Alexander studied at the American Film Institute, where he became interested in directing. His television credits include 32 episodes of Law & Order (on which his stepfather, Edwin Sherin served as an executive producer) and 18 episodes of Rescue Me, in addition to Xena: Warrior Princess, Arli$$, Homicide: Life on the Street, The Practice, Ally McBeal, Third Watch, House M.D., Prison Break, Golden Boy, Jodi Arias: Dirty Little Secret and the pilots for Burn Notice, Warehouse 13, Royal Pains, Edgar Floats, and Three Inches. Alexander was Second Vice-President of the Directors Guild of America, but resigned only two months later following his arrest on child pornography charges. He was replaced by Brooke Kennedy.
Alexander was arrested on July 29, 2015 for the downloading and file sharing of child pornography. The files were found on computers in Alexander’s New York home. The Westchester County D.A. released a statement detailing the nature of the pornography, revealing that examination of his home computers turned up digital files of minors engaged in sexual acts. He was charged with one count of promoting a sexual performance by a child and one count of possessing an obscene sexual performance by a child, facing a maximum of seven years in state prison. The arrest of Alexander came after an investigation in which police downloaded child pornography from an IP address belonging to the Director on July 24. In January 2016, Alexander pleaded guilty to promoting a sexual performance by a child and possessing an obscene performance by a child. In June 2016, he was sentenced to ten years' probation; he must also register as a sex offender in New York.
