Quitman is a city in Cleburne and Faulkner counties in the U.S. state of Arkansas. Its population was 762 at the 2010 census. The portion of t…Quitman is a city in Cleburne and Faulkner counties in the U.S. state of Arkansas. Its population was 762 at the 2010 census. The portion of the city in Faulkner County is part of the Central Arkansas region.