Dynamic response of metallic sandwich structures subjected to water-based impulsive loadings is analyzed experimentally. The effects of the core, the impulsive intensity, and the loading area on the transmitted impulse, transverse deflection, failure modes, and associated mechanisms are identified and quantified. The four kinds of sandwich structures with the weak face–core interface strength are subjected to underwater impulses of three intensities, with a divergent underwater explosive simulator. The results show that the asymmetric failure mode and reverse deformation caused by the counterintuitive behavior are significant failure modes for the sandwich structures. This anomalous response is confirmed to depend on the effects of the core, the impulsive intensity, and the loading area. The core effect influences the magnitude and the asymmetric distribution of transmitted impulse, which is considered as the main reason for the counterintuitive behavior of sandwich structures. The deflection of the sandwich panels, as well as the failure modes, is also discussed.