John Wesley Twichell was born around 1844 in Alexander, New York, to Franklin and Lucy Twichell. His father was a shingle maker who owned $175 of real estate by 1850. The family moved to Milwaukee, Wisconsin, in the 1840s. By 1855, however, Twichell, his mother, and his siblings were living in Boston, New York. By the early 1860s, Twichell was working as a farmer.
He enlisted in the Union army on August 18, 1862, and he mustered in as a private in Company F of the 116th New York Infantry on September 3. According to his service records, he was 5 feet, 5½ inches tall, with light hair and blue eyes. The regiment took part in the siege of Port Hudson. He fell ill in Baton Rouge, Louisiana, in September 1863, and army officials transferred him to Cairo, Illinois. He died there of “chronic diarrhea” on September 22, 1863.