Absalom Graves was born in Culpepper Co. (now Madison Co.), Virginia on 28 November 1768. In 1797 he moved to Boone County and joined the Bullittsburg Baptist Church. On 1 April 1805 he was sworn in as Clerk of the new Circuit Court that replaced the old Quarter Sessions Court.
When the North Bend Association of Baptists formed in 1803, Graves was the Messenger (representative) for Bullittsburg Baptist Church. He was chosen to be the Clerk for the Association, and continued in this role until 1823, when he was appointed Moderator. He continued as the Moderator until his death, and was often appointed to write the Association's circular letters. He compiled a book of hymns for the use of the Association churches in 1825.
Absalom died on the evening of 17 August 1826 following a long illness. He was buried on his own land the following day. The date of the funeral coincided with the annual meeting of the North Bend Association, held in Bullittsburg that year. Given the timing, the funeral was heavily attended by Association members. Two sermons were delivered, one by James Suggett, and the other by John Taylor.