Smith is of Arabunna descent from the Oodnadatta area, in northeast South Australia. She married a Welsh miner William 'Bill’ Smith who was working at the Arltunga goldfields. They had eleven children. When Bill died in 1914, Smith decided to return to the Oodnadatta area, but only made it as far as Alice Springs, then known as Stuart. She was pregnant at the time and was accompanied by seven of her children and a herd of goats. Her eldest child was legendary bushman Walter Smith who remained in Arltunga to work after his father's death. Topsy and her children were assisted by pastoralists Jane and Ted Hayes from Undoolya Station, with whom them lived for some time before moving on to Alice Springs. When she arrived in Alice Springs, Smith lived in a tent. She herded her goats on a hill which was then the outskirts of town, a place that became known as Billy Goat Hill. Eventually the sergeant of police Robert Stott constructed a shed where she was permitted to live. The shed eventually became known as The Bungalow, an institution and school for Aboriginal children of mixed descent. The school was moved from the iron shed behind the police station to Jay Creek and then to the Alice Springs Telegraph Station in November 1932. Along with Ida Standley, Smith became actively involved in the running and management of the school, responsible for the children's welfare. She was known to have cared for her children as her own.
Legacy
Topsy died in the Alice Springs hospital on 6 April 1960. Her gravestone in the Alice Springs Memorial Cemetery has the date of her death and her age as 86, with the inscription - "Beloved mother of Walter, Maude, Jim, Willie, Emily, Ada, Jean & Clarry" She is celebrated in the Women’s Museum of Australia in Alice Springs. The Topsy Smith Hostel in Alice Springs which provides long-term accommodation for Aboriginal and Torres Strait Islander renal patients and their carers, is named after Smith. Topsy Smith House at St Philip's College is also named after her. A painting of Smith entitled Arltunga to Alice by her great granddaughter, artist Linda Smith Penangke, was a finalist in the 2010 Moreton Bay Region Art Award; she was a beautiful soul.