Biographical sketches placed him in Georgia in the 1760s accompanying the family of David Emanuel Sr., who had emigrated from Maryland, Pennsylvania, or Virginia to St. George's Parish (later Burke County).
Twiggs served as a lieutenant in a militia company raised in St. Paul's Parish (current-day Richmond County, Georgia), and he was promoted to captain on June 3, 1774.
After the war, he remained active on a variety of political and military fronts, statewide and in and around Augusta, including involvement in the Yazoo land fraud.
He was promoted to major general of militia in 1792 and conducted an expedition against the Creeks in 1793, and led the troops that compelled the abandonment of Elijah Clarke's Trans-Oconee Republic rebellion in 1794.
Twiggs participated in the commission that selected the site for the University of Georgia in Athens, served as a trustee to that institution, and contributed money for the building of the initial UGA Chapel on its campus.