Beaumont was born in Luzerne County, Pennsylvania, the son of U.S. Representative Andrew Beaumont. He was appointed to the United States Military Academy from the city of Wilkes Barre in 1856 and graduated on May 6, 1861. Ranking 32nd out of his class of 45 cadets, Beaumont was assigned as a second lieutenant to the 1st Cavalry Regiment. Soon after entering the Army he married Margaret Rutter, his childhood sweetheart.