Born in Puerto Rico but growing up in New York City, Elliott had a brief recording career, cutting both albums and singles in the sixties and seventies. He acted and sang for puppet characters in the off-Broadway revue Jacques Brel Is Alive and Well and Living in Paris, as well as the 1975 film version. Other films include Spike Lee's Do the Right Thing (as the Icee man), The Dead Pool (with Clint Eastwood), Impulse (with Lynne Thigpen), Thirteen Conversations About One Thing (with Alan Arkin), and Caught (with Maria Conchita Alonso).
TV work included playing Mr. Fernandez (Alex and Gaby's father) on Ghostwriter, a recurring judge on Law & Order, and appearances on Miami Vice, The Cosby Show, American Family, Hunter, CSI: Miami, and Kidnapped. On Broadway, Elliott was in the original casts of the musicals City of Angels (book by Larry Gelbart) and Marie Christine (with Audra McDonald in the title role).