Born in Alamogordo, he attended Alamogordo and Las Cruces, NM schools. He attended New Mexico A & M (now New Mexico State University), 1930–31 and 1935. He transferred his college credits to the University of Arkansas at Fayetteville and graduated in 1939 in law.
He served as the 15th, 17th and 19th Governor of New Mexico and represented the state in the United States Senate. Mechem was the first person born in the 20th century to become the state's governor, as well as the first person born in New Mexico after statehood to succeed to the office. He later served as a Federal Judge.
He worked as a land surveyor for the U.S. Reclamation Service in Las Cruces from 1932 to 1935. He was admitted to the New Mexico Bar the same year and practiced in Las Cruces and later Albuquerque. He was elected Governor in 1950 and 1952, did not run in 1954, and was elected again in 1956.
In 1954 he ran for the U.S. Senate but was defeated by sitting Senator Clinton Presba Anderson. Mechem lost his bid for reelection on November 6, 1962. He arranged his own appointment (as was his prerogative under the Seventeenth Amendment) to the U.S. Senate when long-time senator Dionisio "Dennis" Chavez died later that month.
In the Senate he voted against the Civil Rights Act of 1964. He served until November 1964 and resumed his law practice after an unsuccessful run for reelection. In 1970 he was appointed by President Richard Nixon as Federal Judge for the U.S. District Court for the District of New Mexico, serving from 1970 to 1982, when he took senior status (1982–2002).
As a judge, Mechem's ruling protected the rights of American Indians on Indian lands from government interference. His father, Edwin Mechem Sr., had been a respected state district judge in Las Cruces.
All human life is sacred and created by God and therefore, we must see all human life as significant and valuable. When governments implement the death penalty, then the life of the convicted person is devalued and all possibility of change in that person’s life ends.
In a society where self-interest, acquisitiveness and individual happiness are often seen as the over-riding interests, the Church, and Christians within it, are called to witness meanings, values and purposes beyond ourselves.
He was an FBI agent from 1942 to 1945 and a member of the New Mexico House of Representatives, 1947-48. A member of the Committee on Government Security, 1956–57, and a member of the American Law Institute, he was again elected Governor in 1960. He was a member of the New Mexico Commission on Reorganization of the Executive Branch and a member of the New Mexico State Police Commission.
Son of Edwin and Eunice (Leard) M. Dorothy Heller, December 30, 1932 (deceased 1972). Children: Martha M. Vigil, John H., Jesse (deceased 1968), Walter M.
Married Josephine Donavan, May 28, 1976.