Scheutz studied law at Lund University, graduating in 1805. He then worked as a legal expert and translator (he translated several works of William Shakespeare) before turning predominantly to politics and mechanical engineering.
He is most known for his inventions; the best known of these is the Scheutzian calculation engine, invented in 1837 and finalized in 1843. This machine, which he constructed with his son Edvard Scheutz, was based on Charles Babbage's difference engine. An improved model, roughly the size of a piano, was created in 1853 and subsequently demonstrated at the World's Fair in Paris, 1855. The machine was then sold to the British government in 1859. Scheutz created yet another machine in 1860, selling it to the United States. The devices were used for creating logarithmic tables.
While the machine was not perfect and could not produce complete tables, Martin Wiberg reworked the construction from the ground up and in 1875 created a compact device which would print complete tables.