Stepan Ivanovich was born in 1718 into the noble Tevyashov family. He was the son of the chamberlain and voivode Ivan Ivanovich Tevyashov (the elder), who lived approximately from 1660 to 1725, and the uncle of the well-known landowner of the Sloboda region, Stepan Ivanovich Tevyashov (the younger).

By 1767, Colonel Stepan Ivanovich Tevyashov owned forty serfs and commanded 4,256 Cossacks, while Brigadier Stepan Ivanovich Tevyashov had sixty serfs and 2,657 Cossacks under his command. He had three sons:

Vladimir Stepanovich (1747, around 1810), who held the position of collegiate counselor;

Vasily Stepanovich (1755, around 1818), second major and leader of the nobility of Ostrogozhsky district in 1794 and 1797;

Ivan Stepanovich (1758, 1817), premier major and leader of the nobility of Ostrogozhsky district in 1786 and 1787, married to Princess Maria Pavlovna Shcherbatova, with whom he had a son, Pavel.

Aiming to fill gaps in his education, Stepan Ivanovich began taking lessons from Grigory Savvich Skovoroda in his mature years. Their lively philosophical discussions, which included Skovoroda, Stepan Ivanovich, and his son Vladimir, are mentioned in Skovoroda's letters and works.

Skovoroda dedicated his work "The Alkiwiad Icon," also known as "The Israelite Serpent," to Stepan Ivanovich Tevyashov and translated Cicero's dialogue "On Old Age" from Latin for him.