Drexel is a city in northwest Bates and southwest Cass counties in the U.S. state of Missouri. The population was 968 at the 2020 census. D…Drexel is a city in northwest Bates and southwest Cass counties in the U.S. state of Missouri. The population was 968 at the 2020 census. Drexel was originally called Stuart City, and under the latter name was platted in 1890. The present name of Drexel was the name of a local store owner. A post office called Drexel has been in operation since 1891.