http://www.mission-sd.com. Mission is a city in Todd County, South Dakota, United States, within the boundaries of the Rosebud Indian Reservation. The population was 1,182 at the 2010 census. Mission is home of the Sinte Gleska University. It is the largest incorporated community in the county, but is smaller than the unincorporated community of Rosebud, the capital of the Rosebud Sioux Tribe.