He was son of William Pitts I (c.1755 – after 1806), a silver-chaser to whom he was apprenticed in 1806, and his wife Mary Armitage.
He ran into business and financial troubles, and committed suicide on 16 April 1840 by taking laudanum at his residence, 5 Watkins Terrace, Pimlico.
Pitts had a very prolific imagination, and In 1830 he executed the bas-reliefs in the bow-room and drawing-rooms at Buckingham Palace.
He made similar drawings to illustrate Horace and the Bacchæ and Ion of Euripides.
In 1846 Joseph executed a bust of George Stephenson that is in the National Portrait Gallery, London.