Ashton is a city in eastern Spink County, South Dakota, United States. The population was 108 at the 2020 census. Ashton was founded in 1879…Ashton is a city in eastern Spink County, South Dakota, United States. The population was 108 at the 2020 census. Ashton was founded in 1879, but it was moved and replatted on the current site in 1881 in order to be located on a new railroad line. The town most likely takes its name after Ashton, England. A post office called Ashton has been in operation since 1879.