Michael Dempsey taught English and religion at Fenwick High School in Oak Park, Illinois, from 1943 to 1950. At the same time he obtained a master's degree in English literature at DePaul University in Chicago. In 1951 he entered the missionary field in Nigeria. He served five terms as pastor and local superior at St. Dominic's Parish in Yaba, Lagos. He was on leave from January 24, 1955, to February 2, 1956. When he returned he was made the Vicar Provincial for the Dominicans of Nigeria. His responsibilities were reduced to Yaba from 1959 to 1962. On August 27, 1965, Dempsey was appointed the vicar of the Nigerian Vicariate.
On July 13, 1967, Pope Paul VI appointed him as the Bishop of Sokoto. He was consecrated a bishop by Cardinal John Cody of Chicago on August 15, 1967, at St. Pius V Church in Chicago. The principal co-consecrators were Archbishop John Kwao Amuzu Aggey of Lagos and Chicago auxiliary bishop Aloysius John Wycislo. He was installed as the diocesan bishop in Sokoto on October 1, 1967, and continued to serve there until his resignation was accepted by Pope John Paul II on December 3, 1984. Prior to his appointment as bishop there were anti-Igbo and anti-Christian riots in 1966 that left the diocese of Sokoto without most of its people, its only indigenous priest fled, and many of its church buildings were destroyed. He focused on the northern part of his diocese where the people remained, and opened the first secondary school in Gusau in 1968. The civil war ended in 1970 and the Catholic people began to return to the Sokoto diocese. The oil industry expanded in the 1970s and that helped to increase the size of the diocese. The Dominican sisters opened a house in Gusau. The catechetical school at Malumfashi trained catechists for northern Nigeria. Successful evangelization efforts were made among the Hausa people. Good relations were maintained with Muslims and other Christian churches. Dempsey suffered several minor strokes toward the end of his time as bishop. He was also the only non-Nigerian bishop in the country. He had to check in and out with the police when he left Sokoto State to enter Katsina State, which was also a part the diocese.
In the autumn of 1985 Dempsey returned to the United States. He took up residence at St. Dominic Priory in Denver, Colorado, and helped out at St. Dominic parish where he ministered to the sick and aged. His health declined and he moved into the Mullen Home, which was operated by the Little Sisters of the Poor in Denver. He died there at the age of 84 on March 19, 1996. Archbishop J. Francis Stafford of Denver celebrated the funeral on March 25, 1996, at St. Dominic's Church. Bishop Dempsey was buried in the Dominican plot at Mount Olivet Cemetery.
