Recently, the Beaufort Gyre has accumulated over 20,000 km3 of freshwater in response to strong anticyclonic atmospheric winds that have prevailed over the gyre for almost two decades. Here we explore key physical processes affecting the accumulation and release of freshwater within an idealized eddy‐resolving model of the Beaufort Gyre. We demonstrate that a realistic halocline can be achieved when its deepening tendency due to Ekman pumping is counteracted by the cumulative action of mesoscale eddies. Based on this balance, we derive analytical scalings for the depth of the halocline and its spin‐up time scale and emphasize their explicit dependence on eddy dynamics. Our study further suggests that the Beaufort Gyre is currently in a state of high sensitivity to atmospheric winds. However, an intensification of surface stress would inevitably lead to a saturation of the freshwater content—a constraint inherently set by the intricacies of the mesoscale eddy dynamics. Key Points Wind‐driven Beaufort Gyre dynamics is simulated within an eddy‐resolving model Mesoscale eddies play a key role in constraining variations in freshwater content The Beaufort Gyre is currently at its highest sensitivity to wind stress forcing