Murphy served as a missionary in the Vice Province of Manaus, Brazil until October 16, 1962 when Pope John XXIII named him to be the first bishop of the newly established Diocese of Juazeiro. He was consecrated a bishop by ArchbishopGerald Thomas Bergan of Omaha on January 2, 1963. The principal co-consecrators were Bishops William Tibertus McCarty, C.Ss.R. of Rapid City, and Glennon Patrick Flavin of Lincoln. Bishop Murphy attended the second and fourth sessions of the Second Vatican Council and was responsible for initiating the Council's reforms in the diocese. He served the Diocese of Juazeiro for eleven years before his resignation for reasons of health was accepted by Paul VI on December 29, 1973. On the same day he was named Titular Bishop of Sululos and Auxiliary Bishop of São Salvador da Bahia. He served the archdiocese until his death on July 6, 1995.[2]