Gut taught at his alma mater of the International College of Saint Anselm in Rome from 1930 to 1939, at which time he became a professor at the Einsiedeln Abbey College. On April 15, 1947, he was elected Abbot of Einsiedeln, receiving the traditional episcopal benediction of new abbots from Archbishop Filippo Bernardini on the following May 5. Gut was elected as the fourth Abbot Primate of the Benedictine Confederation, and thus head of the Benedictine order, on September 24, 1959. From 1962 to 1965 he attended the Second Vatican Council.
On June 10, 1967, Gut was appointed Titular Archbishop of Thuccabora by Pope Paul VI. He received his episcopal consecration eight days later, on June 18, from Eugène Cardinal Tisserant, with Bishops Joseph Hasler and Johannes Vonderach serving as co-consecrators, at Einsiedeln Abbey.
Pope Paul VI created him Cardinal Deacon of S. Giorgio in Velabro in the consistory of June 26 of that same year in advance for his naming as Prefect of Congregation of Rites on the following June 29. Along with Prefect of Rites, Gut also assumed in 1968 the position of president of the consilium for liturgical reform, of which the Benedictine abbot was an advocate. He later resigned as Abbot Primate of the Benedictine Confederation on September 8, 1967. With the dissolution of the Congregation of Rites, the Cardinal became Prefect of the newly-established Congregation for Divine Worship on May 7, 1969.
Gut died in Rome, at age 73. He is buried in Einsiedeln Abbey.