Joseph W. Fletcher was born around 1844 in New Hampshire to Benjamin Fletcher and Lucinda Davis. His father was a carpenter who owned $300 of real estate and $200 of personal property in 1860. The family lived in Nashville, New Hampshire, until the 1850s, when they moved to Chester, Vermont. Fletcher attended school there.
He enlisted in the Union army on July 30, 1862, and mustered in as a private in Company H of the 10th Vermont Infantry on September 1. The army stationed the regiment near Washington, D.C., until June 1863, and he was promoted to corporal on October 19, 1862. The men took part in the Battle of the Wilderness, the Battle of Spotsylvania Court House, and the Battle of Cold Harbor. He served as part of the regimental color guard, and one comrade described him as a “faithful and devoted soldier” who “never us[ed] profane language or indulg[ed] in the many vices that beset the Soldier.” He died at Cold Harbor on June 1, 1864, reportedly “shot on the first instent while bravly fighting in the defence of his Countrys flag.”