Granite Falls is a city in Chippewa, Renville and Yellow Medicine counties in the State of Minnesota.The population was 2,897 at the 2010 census. It is the county seat of Yellow Medicine County. The Andrew John Volstead House, a National Historic Landmark, is located in Granite Falls.he city was named for deposits of granite rock in the area. A post office has been in operation at Granite Falls since 1870. Granite Falls was incorporated as a city in 1889.