Mullins was born in South Pasadena, California on June 13, 1908. He attended the University of Notre Dame, where he played on the football team under head coach Knute Rockne as a fullback from 1928 to 1930. The 1929 and 1930 teams won consecutive national championships, and those teams finished with perfect untied and undefeated records. He graduated from the school with a Bachelor of Arts degree in 1931.
After college, Mullins began his coaching career at the University of Kansas. His first position was as the backfield assistant under head coach Homer Woodson Hargiss in 1931 for a salary of $4,000. The following season, he became head football coach and athletic director at St. Benedict's, a small college in Atchison, Kansas with 600 students at the time, for a salary of about $3,500. While there, he led his teams to a 38–5–1 record. Kansas accounted for two of the five losses. His final season there in 1936, St. Benedict's finished undefeated and untied.
In January 1937, the Loyola University of New Orleans hired Mullins as its head coach. During his three-year tenure, he compiled an 11–16–1 record at Loyola. The Wolves finished the 1939 season with a 5–5 mark, which was sufficient to capture the Dixie Conference championship. In December 1939, he announced that he would not seek renewal of his expiring contract. Two weeks later, the school discontinued its football program. In 1940, he became head coach at Saint Ambrose University in Davenport, Iowa, where he led the football team to an undefeated season.
After American entry into World War II, Mullins entered the United States Navy Reserve. He was sworn in as a lieutenant senior grade in Jacksonville, Florida on March 23, 1942 and then attended a month-long course in Annapolis, Maryland prior to service in the Navy's physical training program. The following year, he assisted Lieutenant Colonel Bernie Bierman, the athletic director and football coach at the Iowa Preflight School. During the 1943 season, he served as the Iowa Pre-Flight backfield coach. By December 1944, Mullins had attained the rank of lieutenant commander and was Iowa Pre-Flight athletic director. In August 1945, he was made a staff officer of the Naval Air Intermediate Training Command in Corpus Christi, Texas. While there, Mullins coached the Naval Air Station football team.
On November 5, 1945, Santa Clara University appointed him as its head coach of its football program, which had been temporarily suspended during the war. However, Mullins tendered his resignation on May 7, 1946 after his abortive five-month search for a residence for his wife and six children in the midst of housing shortage. Mullins returned to Corpus Christi to enter the sporting goods business, but soon reentered the coaching ranks. In 1947, he returned to Saint Ambrose where he served for four more seasons. Mullins led the Bees to another undefeated finish in 1949 with an 8–0 record, and was named the "Little All-American Coach of the Year". In 1950, Saint Ambrose finished 12–1. The grueling 13-game schedule culminated in a victory over Loras to capture the Iowa Intercollegiate Athletic Conference championship. Mullins' career total at the school was 40–7–1.
In February 1951, Kansas State University appointed Mullins as its athletic director with a $9,000 salary. In 1956, Mullins took the same position at Marquette University with a substantial pay raise. The university, which discontinued football and track in 1960, dismissed Mullins on January 31, 1962.
Mullins died of cancer in Chicago on August 10, 1968 at the age of 60. His body was interred in South Bend, Indiana.