Boyd is a city in Lac qui Parle County, Minnesota, United States. The population was 175 at the 2010 census. Boyd was platted in 1884. A …Boyd is a city in Lac qui Parle County, Minnesota, United States. The population was 175 at the 2010 census. Boyd was platted in 1884. A post office has been in operation at Boyd since 1884. The city was incorporated in 1893.