Sara Alderman Murphy was born in Wartrace, Tennessee, on June 17, 1924, the daughter of David M. and Sadie Stephens Alderman. She received a B.A. in Social Studies and English from Vanderbilt in 1945, and a M.S. in Journalism from Columbia University in 1946. In a short autobiography, Murphy relates that at Columbia University she developed a social consciousness on race that she lacked as a young girl in the South; that social consciousness propelled her into social activism later in her life.

She married Patrick C. Murphy, and together they had three children: Ellen, Patrick, and Robert. From 1947 to 1950, Murphy was a member of the faculty of Northwestern State University in Natchitoches, Louisiana. She and her family later moved to Little Rock, where she served on the faculty of the University of Arkansas in Little Rock in 1958. The late 1950's witnessed the eruption of racial tensions in Little Rock, as the city attempted to integrate the whites-only Central High School in the fall of 1957. When Governor Orval Faubus ordered the Little Rock public schools closed in the fall of 1958, a group of women led by Adolphine Fletcher Terry organized the Women's Emergency Committee to Open Our Schools (WEC). Following her convictions opposing racial prejudice, Sara Murphy joined the WEC, serving as a member of its board in 1962 and 1963. When the WEC disbanded in 1963, Murphy redirected her energy into the Panel of American Women (PAW), a multi-ethnic, multi-racial group which sought to lessen racial and religious tensions by promoting understanding through discussion. In 1963 Murphy founded a branch of PAW in Little Rock; her activity in PAW culminated in her serving as vice-president of the national PAW from 1971 to 1974. Murphy's activism earned her recognition among Arkansas's highest governing officials, and from 1972 to 1975 she served as vice-chairperson of the Governor's Commission on the Status of Women.

In 1967 Murphy began working in the Arkansas Department of Education (ADE). Completing her Ed.D. in Education Administration at the University of Arkansas in Fayetteville in 1977, she became the ADE's associate director in 1979. She held that position until 1985, when she became an independent educational consultant working with the Arkansas Educational Renewal Consortium; she served as that organization's executive director in 1987 and 1988.

Murphy renewed her career as an activist in 1982, when she joined Betty Bumpers, the wife of Senator Dale Bumpers, in founding Peace Links, an organization intended to lessen international tensions through exchanges of persons and discussion. She served as the president of Arkansas's Peace Links from 1982 to 1984, and in the late 1980s was instrumental in arranging exchanges between women from the United States and the Soviet Union. Murphy also found a local focus for her activism; from 1989 to 1993 she chaired the advisory committee of the Conflict Management Program at the University of Arkansas at Little Rock. While remaining active in Peace Links, she dedicated the last years of her life to writing Breaking the Silence, a book detailing the role of the WEC in the Little Rock integration crisis. But the onset of cancer prevented her from finishing her book. She died on April 15, 1995; her son Patrick completed the editing of Breaking the Silence.