Vermillion is a city and the county seat of Clay County. It is in the southeastern corner of South Dakota, United States, and is the state'…Vermillion is a city and the county seat of Clay County. It is in the southeastern corner of South Dakota, United States, and is the state's 12th-most populous city. According to the 2020 census, the population was 11,695. The city lies atop a bluff near the Missouri River.