He was ordained by Bishop James Riley of Fargo, North Dakota on June 7, 1916 at his home Parish of St. John the Evangelist in the City of Grafton. As a young priest, Father Mulloy held various posts in the Diocese of Fargo, including: Rector of the Cathedral Parish, Rural Life director, superintendent of education and editor of the diocesan newspaper.
Father Mulloy was chosen as president of the National Rural Life Conference in 1934. On November 11, 1944, Father Mulloy was appointed Bishop of Covington to succeed Bishop Francis Howard. He was consecrated by Bishop Aloysius Muench on January 10, 1945 at St. Mary Cathedral in Fargo. Installation ceremonies took place on January 24, 1945 at St. Mary Cathedral in Covington. During his tenure, many new parishes and schools were established in the suburbs of northern Kentucky. Mulloy also established St. Pius X Seminary and Marydale Retreat Center and Camp, all in Erlanger. In 1954, the Cathedral was elevated to the status of a minor basilica by the pope. After fifteen years of dedicated service, Bishop Mulloy died on June 1, 1959 in Covington. He was laid to rest at St. Mary Cemetery in Fort Mitchell, Kentucky.
Archives of the Diocese of Covington.