Pulpurru was born around the early 1940s. She was born near Yankaltjunku, a rockhole in the northeast Gibson Desert. Her family belong to the Ngaanyatjarra people, for whom Yankaltjunku is a sacred place. Pulpurru grew up living a traditional, nomadic way of life in the desert with her family. They moved from waterhole to waterhole in their traditional country. They lived this way up until the 1960s, by which time they were one of the last groups of nomadic people in Australia. By the mid-1960s, Pulpurru's family were camped at Patjarr, which was only a rockhole at the time. They had been forced to stay in one place because of several years of drought, and Patjarr usually had a reliable supply of water.
Like most other Ngaanyatjarra groups, Pulpurru and her family were moved out of the desert to settle at Warburton. They were brought there by government patrol officers in the late 1960s. At Warburton, Davies worked several domestic jobs. It was at Warburton that Davies began working in arts and crafts, at the Warburton Arts Project. Alongside other women, she learned to paint using modern Western techniques and how to make glasswork designs.
Davies paints events and stories from her country, and the Dreaming legends associated with it. Places often depicted in her paintings are Yankaltjunku (where she was born), Kiwarr (where her family used to dig for water), and Mirra Mirra (where one of Pulpurru's sons was born). She works with paints, tjanpi (grass weaving) and punu (wood carving).
Davies' work has been exhibited across Australia since 1990. It was first shown overseas in 1998, as part of a group exhibition at the Australian High Commission in Kuala Lumpur. She also had work featured in a major group exhibition in China in 2011 (called Tu Di – Shen Ti / Our Land – Our Body).
Davies paintings are held in the National Gallery of Victoria, the Queensland Gallery of Modern Art, the National Museum of Australia and the Kluge-Ruhe Aboriginal Art Collection of the University of Virginia. Some of her paintings are also displayed in the State Parliament building of Western Australia, and in a few major private galleries in Germany and the United States.