(written from a Production point of view)
Rick Mitchell was an assistant film editor for Todd Ramsay on Star Trek: The Motion Picture, along with Randy D. Thornton. He was primarily involved in consolidating with the film's visual effects department, although he was allowed to edit one short sequence. 
After Star Trek, Mitchell worked with that film's director, the late Robert Wise, as editor of the 1980 version of the intra-industry promotional short The Heart of Hollywood. He subsequently served as a contributing editor on Marty Feldman's 1981 comedy In God We Tru$t (which featured cinematography by Charles Correll) and as an assistant editor on the Richard Pryor comedy Bustin' Loose (featuring Bill Quinn and Roy Jenson) and Wes Craven's adaptation of Swamp Thing (starring Adrienne Barbeau and Ray Wise).
In the late 1980s and early 1990s, Mitchell worked as both film editor and sound editor. As a film editor, he worked solely on B-movies and independent films such as Memorial Valley Massacre, Blood Games, and Breathing Fire. His sound work, on the other hand, consisted of more mainstream films, including Die Hard (working with Ron Bartlett, Destiny Borden, Stephen Hunter Flick, Robin Harlan, Bill Henderson, James Simcik, David E. Stone, and Bill Voigtlander), Hoffa (featuring Natalia Nogulich and working with Richard L. Anderson, Joseph F. Brennan, Thomas Causey, John Dunn, Stephen Hunter Flick, Richard Kite, and Nicholas Vincent Korda), and Matinee (1993, starring David Clennon, Dick Miller and Robert Picardo, working with Warren Hamilton, Jr., Ellen Heuer, Mark A. Mangini, John Pospisil, Curt Schulkey and David A. Whittaker and featuring music by Jerry Goldsmith).
During the remainder of the 1990s and the early 2000s, Mitchell focused solely on sound editing, with his credits including In the Mouth of Madness (starring Bernie Casey, John Glover and David Warner; working with Ron Bartlett, John Dunn, Galen Goodpaster, Robin Harlan, Matthew C. May, Howard Neiman, Andrew Patterson, and John Pospisil), Dante's Peak, Anastasia (featuring the voices of Kirsten Dunst, Kelsey Grammer, and Christopher Lloyd), Lethal Weapon 4, and Traffic. He later received two Golden Reel Award nominations from the Motion Picture Sound Editors Guild – one for 2001's Cats & Dogs (which he shared with the aforementioned Richard Anderson and Mark Mangini) and another for 2002's Unconditional Love (also shared with Anderson, as well as David Whittaker). In 2007, Mitchell made a return to film editing with the low-budget horror movie Death's Door.