Born in Roxbury, Massachusetts he was the son of James Mulloy and Anna Cunney on November 17, 1899. He went to Boston Latin High School. For a short time he studied at St. Bonaventure College, Allegheny, New York and contemplated entering the Franciscans. He transferred to Boston College and graduated with honors. He entered the Passionist novitiate and on August 15, 1925 professed his vows and received the name Cletus. He was ordained a priest on June 2, 1928 at St. Patrick’s Cathedral in Newark, New Jersey by Archbishop Thomas Walsh.
Father Mulloy had a distinguished sense about him as a perfect gentleman. He was a tireless student and intelligent conversationalist. He carefully crafted his sermons. He upset some members of the Passionists, when before the age of health clubs, he joined the New York Athletic Club.
He was first assigned to the Passionist Province Mission Band. He began his preaching during the Great Depression. Cost of retreats were $1.00 per weekend. He preached to men, women, seminarians, religious, and the military. He was a favorite of the cloistered Carmelite Nuns. He published articles in the American Ecclesiastical Review and Homiletic and Pastoral Review. He was a popular speaker on The Hour of the Crucified radio show produced by the Passionists which became Crossroads.