Born in Omaha, Nebraska, Beasor joined the Navy in 1952. Following his service he enrolled at the Pasadena Playhouse and started to work as an actor. Since 1980 he is also working as a voice performer and provided his voice to over 350 feature films and television series. Among his first roles are supporting parts in episodes of Salvage 1 (1979, executive produced by Harve Bennett), Paris (1980, with Nicolas Coster), The Incredible Hulk (1980, with Bruce Wright and Terrence Evans), and Foul Play (1981).