David Teviotdale was born at Hyde, Otago, on 17 June 1870, the son of Alexander Teviotdale and his wife, Mary Ann Caldwell. His Scottish father had followed the goldrush from Australia to Otago in 1862. After acquiring sufficient capital, he had bought into the Fourmile Sluicing Company, operating near Hyde, and later purchased a small sheepfarm. Alexander met David's Irish-born mother while she was working at a boarding-house in Hyde.
David was taught at home for several years, becoming a proficient reader and a keen observer of nature. When he was nine he went to school at Hyde, but after four unhappy years he missed the sixth standard entrance examination and persuaded his father to let him leave. He then worked without wages on the family farm and learned the techniques of alluvial goldmining. In 1896 he became engaged to Elizabeth Devlin of Dunedin, and to earn enough money to build a house on the farm he trapped rabbits for the frozen export trade. He and Elizabeth were married in Dunedin on 31 July 1901. However, his father's death in 1904 and Elizabeth's poor health and loneliness led to the sale of the farm in 1905.
From 1905 to 1912 David and Elizabeth worked on a dairy farm near Waitati. In 1912 David became a bookseller and stationer in Palmerston, an occupation that gave him the free time and energy to develop an interest in Maori curios. On early closing days he began to fossick at the Moa-hunter site at the mouth of the Shag River; then as his hobby developed, he regularly spent Sundays at the site. By January 1915 he was recording these activities in his diaries.
About 1920 Teviotdale met H. D. Skinner, the newly appointed curator (later keeper in anthropology) at the Otago University Museum, who advised him to catalogue his finds and to record plans and stratigraphical sections in a diary. Teviotdale joined the Polynesian Society in 1923 and was drawn into the often heated debate on the identity of the Moa-hunters: were they Melanesians, or the Polynesian ancestors of the Maori? In his first article, in the Journal of the Polynesian Society in 1924, Teviotdale described the wide range of Moa-hunter artefact types and practices at the Shag River mouth, which Skinner in an accompanying paper argued were unequivocally Polynesian.
When the Teviotdales moved to Dunedin in 1924, David worked as a newsagent and continued his Sunday curio hunting. After Elizabeth's death in November 1926 he made more-frequent trips, covering a wider range of sites, mainly on the Otago Peninsula. Three more papers and a note were published in the Journal of the Polynesian Society. His commitment to publishing set him apart from the majority of curio hunters, whose knowledge of the provenance of their collections often died with them.
In 1929 Teviotdale finally received professional and academic recognition for his work: the Otago University Museum employed him as Skinner's assistant, and the University of Otago awarded him the Percy Smith Prize in Anthropology for his field work and papers. His museum duties were split between registration of artefacts and field work to collect more. Professional employment allowed him to prepare more publications, the most significant being his synthesis of the material culture of the Moa-hunters of Murihiku (1932). The paper, which produced evidence supporting the Polynesian ancestry of the Moa-hunters, raised considerable debate in the Polynesian Society.
For the first time Teviotdale was able to visit local sites on weekdays, and he increasingly applied goldmining methods to get at deep artefact-bearing deposits. He also undertook prolonged trips to Southland, South and North Otago, Banks Peninsula, Marlborough and Nelson. His longest period at one site was 87 days spent at Selwyn Hovell's notorious excavation at Oruarangi pa, near Thames, in the summer of 1932–33. There is strong evidence in Teviotdale's diary that Hovell removed burial goods from the cemetery on the site; his actions resulted in a court case.
When Teviotdale retired in 1937 the Otago University Museum appointed him honorary archaeologist, thereby continuing a relationship that had enhanced the museum's collections by several thousand artefacts. In 1942 Teviotdale took over as director of the Southland Museum, Invercargill, a post he held until he was 82. Throughout this period he continued to collect artefacts, travelling by train to the windswept beaches of Foveaux Strait.
In his latter years David Teviotdale suffered from Parkinson's disease. He died in Invercargill on 28 December 1958, survived by a daughter. Despite a lack of formal education, he had become a professional archaeologist and museum director, respected for his industriousness and contributions to New Zealand archaeology.