Mort's father was a stockbroker, and he initially also pursued a career in finance. Abrahams grew interested in cinema while working at Bank Of America, tasked with selling a few flopped TV productions financed by the bank. Abrahams debuted in October 1950 as a producer of Tom Corbett, Space Cadet TV series on [url=https://discogs.com/label/567392]CBS[/url], following the show to [url=https://discogs.com/label/12220]ABC[/url] network in early 1951; Mort also worked on ABC's Tales of Tomorrow sci-fi anthology (1951 to 1953). Abrahams produced several TV shows at Bank Of America, including the live G.E. Theatre anthology hosted by Ronald Reagan and starring James Dean and Natalie Wood, among others. In the 1960s, he worked for Herbert B. Leonard's production, responsible for the on-the-road adventure series Route 66 (1962–63). Mort later joined the [url=https://discogs.com/label/259148]NBC[/url] network, where he produced The Man from U.N.C.L.E. spy fiction TV series in 1964 and 1965; he briefly served as Vice President at Ray Stark's Rastar Productions in 1969–71. Abrahams co-authored the screenplay for Beneath the Planet of the Apes with Paul Dehn in 1970, the sequel for Franklin J. Schaffner's 1968 blockbuster Planet of the Apes produced by Arthur P. Jacobs.

In 1972, Mort Abrahams joined the American Film Theatre company as an executive producer, responsible for eight film releases in just ten months, including [url=https://discogs.com/artist/3657637]John Frankenheimer[/url]'s The Iceman Cometh and A Delicate Balance by [url=https://discogs.com/artist/4705496]Tony Richardson[/url] starring Katharine Hepburn and Paul Scofield. In the later years, Abrahams primarily worked on telefilms, such as Separate Tables (1983), written by Terence Rattigan and directed by John Schlesinger, starring Julie Christie, or the adaptation of Erich Maria Remarque's Arch of Triumph novel with Anthony Hopkins, directed by Waris Hussein in 1984. His last job was in 1988, producing Seven Hours to Judgment crime drama by Beau Bridges.