Organ Mountains-Desert Peaks National Monument Correction Act - Prohibits construing either the national monument designation or any management plan in furtherance of the Organ Mountains-Desert Peaks National Monument, New Mexico (designated on May 21, 2014) as: (1) preventing the Secretary of Homeland Security from undertaking law enforcement and border security activities within the areas designated as the Monument, including the ability to use motorized vehicles within it; (2) limiting the 2006 Memorandum of Understanding among the Department of Homeland Security (DHS), the Department of the Interior, and the Department of Agriculture (USDA) regarding cooperative national security and counterterrorism efforts on federal land along U.S. borders; (3) preventing the DHS Secretary from conducting low-level overflights over the Monument for law enforcement and border security purposes; or (4) preventing the Secretary of the Interior from allowing within the Monument the installation and maintenance of communication or surveillance infrastructure necessary for law enforcement or border security activities.

Makes the route excluded from the Potrillo Mountains, identified as "Restricted--Administrative Access" on the map entitled "Potrillo Mountains Complex," dated December 10, 2013, available for administrative and law enforcement uses, including border security activities.

Specifies that nothing in the national monument designation or any management plan in furtherance of the Monument shall restrict or preclude low-level overflights of military aircraft, the designation of new units of special airspace, or the use or establishment of military flight training routes, over the Monument.