Stephen Mathewson Green was born in Scituate, R.I., in 1840, to Stephen A. Greene and Susan Mathewson. The Greenes were long established in the greater Warwick, R.I. area and Stephen M. Greene's great-grandfather Benjamin fought in the Revolutionary War. Stephen joined up with the original group of men who comprised Battery A of the First Regiment of R.I. Light Artillery soon after the outbreak of the Civil War, on June 6, 1861. He is listed as a gunner and was also sergeant in Battery A, being promoted to that rank on August 3, 1863. He served in several prominent battles of the Army of the Potomac, in the course of which the R.I. Light Artillery earned a reputation for efficiency and outstanding performance. He served as a recruiter in Rhode Island from mid-February to mid-April of 1864, and was mustered out on June 17th of that year.
After the war, Greene apparently worked as a machinist in Providence and North Providence, but later became a dairy farmer with a farm on Woodward Road in North Providence. He married Sarah W. Olney on January 11, 1866. She was the daughter of Henry D. and Susan (Angell) Olney, the Olneys and Angells being two prominent Providence families. The Greenes had three boys: Clarence Henry (1867-1945), Frederick Albert (1869-1913), and Stephen Mathewson (1879-81). Greene served as a master of Mt. Vernon Lodge, A. F. & A. M., a member of the Providence Royal Arch Chapter, and St. John's Commandery, No. 1, K.T., Providence, RI. Greene passed away October 2, 1912.