Truxton is a town in Cortland County, New York, United States. The population was 1,133 at the 2010 census. The town is named for Commodore Thomas Truxtun, a privateer in the American Revolutio…Truxton is a town in Cortland County, New York, United States. The population was 1,133 at the 2010 census. The town is named for Commodore Thomas Truxtun, a privateer in the American Revolution and one of the US Navy's first commanding officers.