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. A post office called Puxico has been in operation since 1884. Puxico was incorporated as a town in 1884.