Steuchius grew up in Härnösand in northern Sweden, where his father Petrus Steuchius was superintendent. He was ordained to priest in 1672 and participates in the Riksdag of the Estates in 1672 and 1675. In 1676 he became professor of logics and metaphysics at the Uppsala University. He married in 1680. In 1683 his father died, and Mathias superseded him. He worked as superintendent for twelve years, and put much effort into bringing Christianity and education to the indigenous Sami people.
In 1693 he was made doctor of theology in Uppsala, and in 1694 promoted to professor. But already in June 1694 he was summoned to Lund, to be appointed Bishop of Lund.
At the death of Haquin Spegel, Steuchius was elected new archbishop in 1714. He worked in Uppsala until his death in 1730.
Steuchius was known as a devoted and righteous man by his way of living and teaching.