Stevenson was born in Boston, Massachusetts. He was 25 years old when the Civil War began and had risen from private to major in the Massachusetts Militia at that time. On December 3, 1861 Stevenson was appointed colonel of the 24th Massachusetts Volunteer Infantry. He led his regiment in the battles of Roanoke Island and New Bern. Following the capture of New Bern significant Union reinforcements arrived in North Carolina and Stevenson assumed command of a brigade under John G. Foster.