Henry was the youngest son of Mary Ann and Pashur (Harry) Copcutt of Gladstone Street, Hobart. When he enlisted in April 1918, his two older brothers had already seen service with William being killed in action at Pozieres whilst serving with the 26th Battalion. He was posthumously awarded the Military Medal. Arthur was an original member of the 40th Battalion and returned home in July 1917 having been wounded in action. No doubt Mary Ann was reluctant to allow her youngest son to go.
After a period of training at Claremont, Henry travelled to Sydney where he boarded the HMAT A14 Borda on 17 June 1918, the vessel arriving in London on 27 September 1918. In October he was transferred to Heytesbury to join the artillery details. With the withdrawal of many units, but still keeping a presence in France, Gunner Copcutt was taken on strength with the 1st Field Artillery until the end of March 1919 when he too was detached to the Graves Registration Detachment. He returned to August in July and was discharged in September.
While Henry returned to Hobart for discharge, by 1922 he had left to work at Circular Head and from there appears to have gone to the mainland. Henry Copcutt served in World War 2, enlisting in New South Wales. He spent just over two years serving with the 22nd Garrison Battalion.