He was ordained as a priest in 1771. After the dissolution of the Abbey, he took over the faculty for Natural Science, Geography and Mechanics at the Imperial Scientific Academy. In 1788 he was appointed Assistant Director of the Natural Science Collection. In 1797 he became Imperial Counsellor and Deputy Director of the Collection (together with Ludwig Balthasar von Baillou). After the death of Ludwig Balthasar von Baillou, Stütz became the only Director of the Mineral Cabinet.