Ordained to the priesthood in Rome on December 20, 1967, Schwietz earned his Licentiate of Sacred Theology from the Pontifical Gregorian University in 1968. He served as associate pastor of St. Thomas Aquinas parish in International Falls from 1975 to 1978, when he was named Director of the College Seminary program for his religious order at Creighton University. In 1984, he became pastor of Holy Family parish in Duluth.
On December 12, 1989, Schwietz was appointed the seventh Bishop of Duluth by Pope John Paul II. He received his episcopal consecration on February 2, 1990 from Archbishop John Roach, with Bishops Robert Brom and Michael Pfeifer, OMI, serving as co-consecrators, in the Cathedral of Our Lady of the Rosary. Schwietz was awarded an honorary doctorate in humanities from Lewis University in 1998.
In August 2005, he attracted the attention of Traditionalist Catholics when he refused to permit Fr. Andrew Szymakowski, FSSP, to celebrate the Tridentine Mass at the latter's parish assignment within the archdiocese.
Schwietz currently serves as Episcopal Moderator for Teens Encounter Christ movement, having held this position since 1991. On October 2, 2006, Guzman Carriquiry, Undersecretary of the Pontifical Council for the Laity, met with the Archbishop, who presented Teens Encounter Christ to the Curial dicastery. He also served as Episcopal Liaison to Region I of the National Association of Catholic Chaplains
Within the United States Conference of Catholic Bishops, he served as a consultant to the Liturgy Committee (1991-1994), member (1992-2004) and chairman (elected 1998) of the Vocation Committee, and member of the Committee on the Laity (1995-1998) and chairman of its Subcommittee on Youth (1993-1998). He has also sat on the Catholic Relief Services' Board of Directions (1997-2003) and the NCCB Administrative Board (1994-1997, 1998-2002). In 2002, he became Regional Representative on the Board for the American College in Leuven, Belgium.