The dynamic response and the failure of the different composite structures subjected to impulsive loadings are performed experimentally with metallic foam projectile. The composite lattice core based sandwich structure is reinforced with polyurethane foam and shows a significant improvement in impulsive mitigation. The effects of core and loading intensity are carried out to identify and quantify the dynamic response, failure mode, and energy absorption efficiency of the composite structures. The results show that the foam filled lattice sandwich has an outperformed deflection resistance and remains better intact due to the loading transferring and weak effect of localization of the out-of-plane deflection. Although the energy absorption efficiency per unit mass of the lattice/foam sandwich is lower, the energy absorption capacity of the structure is confirmed to have been improved significantly, and the difference in the efficiency decreases noticeably with the increasing impulsive intensities. Both the sandwich structures have superior performance of impulsive resistance in comparison with the composite laminate.