This research investigated the failure behaviors of the composite sandwich structures with face sheet and core debond subjected to compressive loading. Experiments and numerical simulations were conducted to determine the effects of the face sheet thickness and debond length on the compressive strength and failure mechanisms of the composite sandwich structures. Experimental results revealed that sandwich structures with either thicker face sheets or a shorter debond length exhibited a higher buckling load and greater failure strength. Moreover, when the debond length was short, failure was primarily caused by global buckling; conversely, when the debond length was long, failure was caused by local buckling and crack extension from the debond edge. To characterize the failure mechanism, a nonlinear finite element simulation of sandwich specimens containing imperfections was conducted. The simulation revealed that, when the dominant failure mode was global buckling, failure occurred at the intermediate portion of the foam core and strength could be characterized using the maximum principal strain criterion. However, when the failure mode was local buckling, failure was initiated at the debond tip, and strength could be predicted using the damage zone method.