Elephant Butte, NM. Online Offers. Elephant Butte is a city in Sierra County, New Mexico, United States, near Elephant Butte Reservoir and State Park. The population was 1,390 at the 2000 census. Elephant Butte is located at 33°11′23″N 107°13′22″W / 33.18972°N 107.22278°W / 33.18972; -107.22278 (33.189809, -107.222873). According to the United States Census Bureau, the city has a total area of 3.0 square miles (7.7 km²), all of it land.