Mitchell was accepted into Columbian University (later renamed George Washington University) in Washington, D.C., dropped out to join the United States Army during the Spanish-American War, and eventually graduated from the school. While there he was a member of Phi Kappa Psi Fraternity. Upon dropping out of Columbian at age 18, he enlisted in the United States Army as a private and was mustered into Company M of the 1st Wisconsin Infantry Regiment on May 14, 1898. Mitchell was immediately assigned and mobilized into Brigadier General Arthur MacArthur's command in the Philippines, where MacArthur was placed in charge of the Department of Northern Luzon in the spring of 1899. Mitchell participated in operations against Filipino insurgents in northern and central Luzon at the end of the Spanish-American War and during the Philippine–American War. He quickly gained a commission due to his father's influence and joined the U.S. Army Signal Corps.