Joseph Ambrose Murray was born in Wilkes-Barre, Pennsylvania, on November 11, 1920. He attended Law School at the University of Pennsylvania in 1945, but did not play baseball for Penn.
Murray was signed as an amateur free agent by the New York Yankees before the 1940 season. Before the 1948 season, he was sent from the New York Yankees to the Washington Senators; before the 1949 season, he was passed on from the Senators to a team in West Palm Beach, in the Florida International league. Before the 1950 season, the Philadelphia Athletics obtained him from West Palm Beach. He made his major league baseball debut on August 17, 1950. He pitched just thirty innings with the Athletics before his major league career ended.
He died in San Clemente, California, on October 19, 2001.