Semen studied at the Azov Province Survey Expedition. One of his first military posts was as a surveyor in Tavrida province (with the rank of ensign). He participated in the storming of Anapa, and in the suppression of the "confederates" in Poland in the early 1790s. He later served in the Mariupol Hussars regiment, and in 1797 was sent to conduct topographical surveys of Crimea and the Black Sea provinces. In the next decade Mukhin produced a general map of the empire. Talented but with a flawed work ethic, Mukhin was demoted from the heights of quartermaster-general to the post of chief of the Cartography Depot in 1812. His major assignment was the topographical mapping of Crimea, to which he devoted himself in 1816, producing his renowned map of 1817.