Enoch Leavitt was born around 1844 in Ohio to Daniel Leavitt and Sophia Freeman. His father was a farmer who died around 1851. Leavitt grew up and attended school in Spencer, Ohio, and by 1860, he was working as a farmer. He enlisted in the Union army on August 25, 1861, and mustered in as a private in Company H of the 2nd Ohio Cavalry on October 8.
The regiment took part the Battle of Cumberland Gap, the Knoxville Campaign, the Battle of the Wilderness, the Battle of Spotsylvania Court House, the Shenandoah Valley campaign of 1864, and the Appomattox campaign. He was eventually promoted to corporal, and he mustered out in Baltimore, Maryland, on May 25, 1865. He returned to Ohio after the war and attended school in Hiram, Ohio. He applied for a federal pension in June 1865 and eventually secured one.
Leavitt married Julia A. Smith on June 24, 1873, and they had at least four children: Minnie, born around 1877; Edward, born around 1879; Freeman, born around 1881; and Thomas, born around 1884. The family moved to Morris, Minnesota, around 1878, and Leavitt worked as a farmer there. They moved to Eden Lake, Minnesota, in the 1890s. He died in Minnesota around 1907.