The son of Patrick and Anne Glennon, Joseph was born in Wigan, Lancashire, in 1880. By 1911, he was still living in Wigan, with his wife, Mary Jane Glennon. He later moved to Westbury Street, Wolverhampton, and became a member of Wolverhampton Central Conservative Club, as well as playing billiards and being a Staffordshire county bowler.
Joseph enlisted as a Sergeant in the 8th Service Battalion of the South Staffordshire Regiment (number 11167). Over the course of his service, he was wounded four times and gassed once, and the latter caused him to be unconscious for five days. In 1916 he was in charge of trench mortars when he was wounded by a hand grenade in France. He died from these wounds at Number 17 Casualty Clearing Station in Belgium on 9 February 1916. News of his death was reported in the Express & Star on 2 March 1916. He is buried in the Lijssenthoek Military Cemetery in Belgium.