In this work, a protective structure with 2A12T4 aluminum alloy as the panel material and plywood as the core layer was designed. Penetration experiments were performed by firing multiple projectiles from a light gas gun. The impact behavior, damage mode, absorbed energy, and residual strength of the interlayer after impact were studied. The dynamic response and the failure of the interlayer were analyzed. Disbonding, fiber fracture, buckling, shear, and core fracture between the metal layer and the composite layer of the front panel were observed. The impact resistance of the sandwich plate was also studied. Based on the results of the experiments and numerical simulations, failure determination of the plywood core layer was achieved using the Hashin criterion, and a finite element model was established using ABAQUS software. High-speed impact testing was performed with a Hopkinson pressure bar. The stress–strain relationship under a high dynamic strain rate is given here, and the energy absorption efficiency under loading in different directions was analyzed. Finite element analysis of the representative volume elements in the wood microstructure was also carried out. The results reported here can be used to guide optimal design of sandwich structures suitable for use under high-speed impact conditions.