Amos Woodworth was born on May 4, 1741 in Salisbury, Litchfield, Connecticut. He was the son of Jane Munger (1705-1774) and Caleb Woodworth (1704-1780). On April 12, 1764, he married Eunice Newland (1748-1820) in Salisbury, Connecticut. Eunice was the daughter of Abigail Babbit and Joseph Newland.
Amos served as a private in the Revolutionary War under his brother, Captain Ephraim Woodworth, Colonel Cornelius Van Veghten's 4th Company, 13th Regiment, Albany County, New York. He took part in the capture of Burgoyne at Saratoga in the Battle of Bemis Heights.