Puxico is a city in Stoddard County, Missouri, United States. The population was 881 at the 2010 census. Puxico was first settled in 18…Puxico is a city in Stoddard County, Missouri, United States. The population was 881 at the 2010 census. Puxico was first settled in 1883, and named after Pucksicah, an Indian chief. Early settlers include W. C. Clark, E.L Hawks, George Eaton and J.A Hickman. A post office called Puxico has been in operation since 1884. Puxico was incorporated as a town in 1884.