Arthur M. Stone was born on October 31, 1844, in Spencer, Massachusetts, to Albert Stone and Martha L. Powers. His father was a boot maker. Stone grew up and attended school in Spencer, and he enlisted in the Union army on July 19, 1862. Two weeks later, on July 31, he mustered in as a corporal in Company E of the 34th Massachusetts Infantry. The regiment took part in the Battle of Cedar Creek, the siege of Petersburg, and the Appomattox campaign. He mustered out in Richmond, Virginia, on June 16, 1865.
Stone returned to Spencer after the war and began work as a clerk. He married Mary L. Dunton there on September 4, 1869, and they had at least three children: Mabel, born around 1870; Ruth, born around 1875; and Gertrude, born around 1881. The family settled in Leicester, Massachusetts, and by 1870, Stone was working as a cashier in a bank. They owned at least $4,200 of personal property. A decade later, they were living in Worcester, Massachusetts, and Stone was working as a boot manufacturer. He applied for a federal pension in December 1906 and eventually secured one. Mary died in Worcester in 1909, and he followed on June 12, 1912.