Joseph Graves was born 20 June 1773 in Culpeper Co., Virginia. He moved to Kentucky with his family in about 1797. He married Malinda Watts, daughter of Johnson Watts and Susan Davis of Boone County on 4 May 1812.
Graves became Sheriff in October 1820. He chose as his deputy Philip S. Bush. In July of the same year he chose additional deputies, William Cave, and Washington Watts. His older brother, Absalom Graves, pastor of the Bullittsburg Baptist Church, was Clerk of the Courts for many years.
Joseph Graves died 22 April 1836 in Boone County.