As a young man, Alexander Stuart made numerous voyages on sailing vessels before emigrating to America in 1860. He is believed to have attended rugby and served in the British Navy. He is listed as an artist in the New York directories between 1860 and 1863, when he enlisted in the U.S. Navy.
Throughout the Civil War he served aboard union vessels, including the light draft monitor U.S.S. Yazoo. Of the many accurate battle scenes he portrayed depicting Civil War engagements, very few come on the market. After being discharged in Philadelphia in 1866, the sailor-artist set up shop along the banks of the Delaware river, a major shipbuilding locale then known as the "Clyde of America".
In later years, Stuart created many ship portraits for shipbuilding firms on the Delaware, most notably Harlan & Hollingsworth and Reany, Son & Archibald who specialized in ships for the Mallory and Pacific mail lines. These portraits along with his Civil War battles scenes are considered to be his most important work.