Rabbi David Tevel, son of Rabbi Nathan Neta, was born in Brody into a rabbinic family; his father was head of the rabbinical court of Brody. He descended from Rabbi Binyamin Aharon Slonik, author of Masat Binyamin, and from the Maharal of Prague. His brother, Rabbi Aryeh Leib, became head of the court of Anikšt, and his sister married Yitzchak Chayot, a leader of the Brody community. He himself married the daughter of Rabbi Tzvi Hirsch, one of the notables of Brody.

He first served as rabbi of Sasslov in Volhynia. In 5527 (1767) he was appointed rabbi of Horochow, where he headed a large yeshiva; among his students was Rabbi Baruch Teomim-Frankel, whom he called "the head of the students." In 5534 (1774) he was elected rabbi and Av Beit Din of Lissa (Leszno), where he also led a yeshiva; Rabbi Chaim Davidsohn, later rabbi of Warsaw, studied there. Jews throughout the Diaspora turned to him with halachic questions.

Though he had reservations about Chassidism, according to Aharon Walden he dissuaded his friend the Noda BiYehuda from banning and burning the book Toldos Yaakov Yosef, at the request of the brothers Rabbi Pinchas Horowitz and Rabbi Shmelke of Nikolsburg. He was one of the ten leading rabbis who gathered in Brody to support Rabbi Yisrael Lipschitz's ruling in the Cleves divorce affair.

In 5542 (1782) he joined the Noda BiYehuda in the struggle against the Haskalah. In his Shabbat HaGadol sermon he attacked Naftali Herz Wessely, whose pamphlet Divrei Shalom VeEmet praised Emperor Joseph II's plan for German-language Jewish schools, and he withdrew the approbation he had given to Wessely's book Yein Levanon. Maskilim denounced him to the authorities, and the Noda BiYehuda demanded that the leaders of the Berlin community dissociate themselves from the complaints.

Works: his only printed book is Nefesh David on the Torah, followed by a short treatise called Michtav LeDavid; many of his responsa appear in the works of his contemporaries, such as the Noda BiYehuda, Tiferes Tzvi and Beis Meir.

He passed away on 16 Tevet 5552 (11 January 1792). In his will he asked that Rabbi Yaakov Lorberbaum succeed him as rabbi of the city; his son, Rabbi Zechariah Mendel, served there as deputy head of the court until 5565 (1805).