Glacier-front dynamics is an important control on Greenland's ice mass balance. Warmer ocean waters trigger ice-front retreats of marine-terminating glaciers, and the corresponding loss in resistive stress leads to glacier acceleration and thinning. Here we present an approach to quantify the sensitivity and vulnerability of marine-terminating glaciers to ocean-induced melt. We develop a plan view model of Store Gletscher that includes a level set-based moving boundary capability, a parameterized ocean-induced melt, and a calving law with complete and precise land and fjord topographies to model the response of the glacier to increased melt. We find that the glacier is stabilized by a sill at its terminus. The glacier is dislodged from the sill when ocean-induced melt quadruples, at which point the glacier retreats irreversibly for 27 km into a reverse bed. The model suggests that ice-ocean interactions are the triggering mechanism of glacier retreat, but the bed controls its magnitude.