He was the eldest son of Robert Spearman, attorney of Durham, by his wife Hannah, only daughter of William Webster, merchant, of Stockton-on-Tees.
[1] He studied at Durham School and Corpus Christi College, Oxford, but left without taking a degree.
[1] A pupil of John Hutchinson, Spearman survived him, edited his works, and wrote his life.
[1] He was the dedicatee of Two Dissertations concerning the Etymology and Scripture-Meaning of the Hebrew words Elohim and Berith (1751) by Thomas Sharp, with whom he was on good terms.
[2] Spearman died on 20 October 1761, leaving only female issue by his wife Anne, daughter of Robert Sharpe of Hawthorn, County Durham.