Murphy, one of seven children, was born in Winnipeg in 1932. His father, William Murphy, a senior executive with Coca-Cola, moved the family to Vancouver. He attended Vancouver College, a K-12 independent Catholic school for boys served by the Congregation of Christian Brothers in British Columbia, where he was a football standout. He then starred with the University of British Columbia Thunderbirds as a left-handed quarterback and defensive back, and played a brief stint with the British Columbia Lions of the CFL in 1956. Murphy then turned to education, returning to Vancouver College and taking over the reins as Head Coach in 1960–61. He led the Fighting Irish to their only undefeated season. He pursued his master's degree while an assistant coach at Eastern Washington University under Head Coach Dave Holmes. Murphy followed Holmes to the University of Hawaii Rainbows, and became part of the most successful coaching tenure in Hawaii history. (From 1968–1974, UH won 67 percent of its games and never suffered a losing season.) In 1973, Murphy left Hawaii for the San Jose State Spartans under Head Coach Darryl Rogers.
In 1983, Murphy was hired by Paul Robson of the Winnipeg Blue Bombers and spent 14 years as Head Coach and General Manager. He developed a reputation for finding top talent, and developed one of the most feared defenses in CFL history with the likes of Tyrone Jones, James "Wild" West, and Aaron Brown. In a controversial move, he traded away strong-armed and popular starting QB Dieter Brock to the Hamilton Tiger-Cats for the smarts of lesser known QB Tom Clements. Although Clements would suffer a season-ending collarbone injury, and the Bombers would lose in the 1983 Western Final to the BC Lions, they would crush the Brock-led Tiger-Cats in 1984 by a score of 47–17 in a frigid Grey Cup in Edmonton, bringing the city of Winnipeg its first Grey Cup in 22 years.
After suffering heart attacks in 1978 and 1985, in 1992 Murphy underwent emergency heart bypass surgery that kept him alive before being saved by a last-second donor and successful heart transplant surgery. In January 1993, the Governor General of Canada presented Cal Murphy with the 125th Anniversary of the Confederation of Canada Medal in recognition of the significant contribution to compatriots, community and to Canada. His eldest son, Mike, is a scout with the NFL's Miami Dolphins, and son-in-law, Sammy Garza, is a scout with the NFL's Dallas Cowboys. He had seven children: Carol, Mike, Barbara, Erin, Shannon, Brian and Kelly.