Quitman is a city and the county seat of Wood County, Texas, United States. Its population was 1,942 at the 2020 census. The city was na…Quitman is a city and the county seat of Wood County, Texas, United States. Its population was 1,942 at the 2020 census. The city was named for John A. Quitman, a veteran of the Mexican–American War, and once governor of Mississippi.