Tevyashov came from the Tevyashov family. He was the son of the Ostrogozhsk colonel Ivan Ivanovich Tevyashov (the younger), born around 1700 and died after 1765, and the nephew of the Kharkov colonel Stepan Ivanovich Tevyashov (the elder), who lived from 1718 to 1790. He was baptized in honor of Stephen of Surazh.

After the Seven Years' War, Brigadier Tevyashov retired and managed his estates. In 1766, he led the settlement of German colonists in the Ostrogozhsk region, and the following year he was elected a member of the Legislative Commission from the nobility of the Ostrogozhsk province.

Researchers believe that in the Kharkov home of his friend and relative Yevdokim Shcherbinin, Tevyashov met the philosopher Grigory Skovoroda. Subsequently, Skovoroda often visited the Tevyashovs and maintained close relations with family members, including Colonel Stepan Ivanovich Tevyashov (the elder) and his son Vladimir Stepanovich Tevyashov. It is known that Tevyashov had a large collection of rare books and manuscripts, which Skovoroda could have accessed in his home.

From his marriage to Countess Maria Santi, daughter of the chief master of ceremonies Franz Matveevich, Brigadier Tevyashov had two daughters: Praskovya and Yevdokiya. Yevdokiya Stepanovna, born in 1770 and died in 1827, brought into her marriage with Dmitry Vasilyevich Chertkov 13,950 peasants of both sexes and 200,000 desyatins of land in the Ostrogozhsk, Boguchar, and Valuy districts. Their children Alexander, Nikolai, and Ivan Chertkov left a significant mark in Russian history.