Mesoscale eddies are ubiquitous in the ocean and dominate the ocean's kinetic energy. However, physical processes influencing ocean eddy energy remains poorly understood. Mesoscale ocean eddy-wind interaction potentially provides an energy flux into or out of the eddy field, but its effect on ocean eddies has not yet been determined. Here we examine work done by atmospheric winds on more than 1,200,000 mesoscale eddies identified from satellite altimetry data, and show that atmospheric winds significantly damp mesoscale ocean eddies, particularly in the energetic western boundary current regions and the Southern Ocean. Furthermore, the large-scale wind stress curl is found to on average systematically inject kinetic energy into anticyclonic (cyclonic) eddies in the subtropical (subpolar) gyres, while mechanically damps anticyclonic (cyclonic) eddies in the subpolar (subtropical) gyres.