Joseph Smith was born in Blackburn, Lancashire, England in c.1862. In the 1891 England and Wales Census his occupation is given as Engineer and Architect, however it is not known where or with whom he received his training. In the 1890s he formed an architectural partnership with Henry Arthur Cheers (1853-1916). It is unclear if this was a formal partnership. They appear to have had an office at 24 Richmond Terrace, Blackburn, Lancashire, where Smith was based, and in Twickenham, Middlesex, where Cheers had been in practice since the early 1880s.
Smith's address was given as 144 Revidge Road, Blackburn, Lancashire in 1901 and Elsinore, Wilpshire, Lancashire in 1911
Work by Cheers and Smith in partnership included Halifax Public Hall (1896), and East Ham Public Hall (1903). In 1909 they won a competition to design Colchester Technical Institute. Their designs are illustrated in British Competitions in Architecture vol. 2, no. 22, June 1909 (pp. 329-332). There is no evidence that the Institute was built.