Tubb lived at Lavender Cottage in Warborough, a village near the town of Dorchester. He wished to become a wood carver, but his father convinced him to become a maltster. He lived a country life as a bachelor.
Tubb's main legacy was to carve a poem on a large beech tree on the eastern side of Castle Hill at Wittenham Clumps. He took a tent and a ladder to Castle Hill and spent the summers of 1844 and 1845 carving the letters of a 20-line poem. The poem demonstrates Joseph Tubb's passion for the Oxfordshire countryside. Discrepancies in wording between a written original and those on the tree are said to be because he carved from memory.