He was ordained to the priesthood on May 30, 1976. After his ordination he worked as a parish priest in Panevėžys and in the parish of the Holy Spirit in Vilnius (from 1981). On April 13, 1991, Pope John Paul II appointed Kaškievič to the newly formed Diocese of Grodno. On May 23, 1991, he was ordained a bishop, consecrated by archbishop Tadevuš Kandrusievič. In 2006-2015 Kaškievič was chairman of the Conference of Catholic Bishops of Belarus. He is also the head of the Council of Youth Affairs and the Council for Catholic Education.