Joseph Archer emigrated to the Cape Colony about 1890 and joined the Cape Government Railways, first as a foreman and later as station-master at various stations. When he eventually became station-master at Matjiesfontein he developed a rock garden of Karoo plants which repeatedly won the South African Railways prize for the best station garden in the country. In 1925 he left the railways to take up an appointment as the first curator of the Karoo Garden laid out in the early nineteen twenties near the station Whitehill, about five kilometers from Matjiesfontein, as a branch of the National Botanic Gardens at Kirstenbosch. With prof. R.H. Compton, the Director of Kirstenbosch, and others Archer undertook several collecting trips in the Karoo, the north-western parts of the Cape Province and Namibia, bringing together a large and representative collection of succulents and other plants from these regions. He also successfully cultivated many of these plants at Whitehill. He retired as curator in 1939, after which the garden was moved to a more accessible site at Worcester.
Archer did much to promote the popularity of succulent cultivation in South Afrca. Several plant species were named in his honour, including Crassula archeri and Kleinia archeri.