An innovative auxetic-cored sandwich panel (AXP) is proposed. Its perforation resistant performance under high-velocity projectile impact was numerically analyzed using the validated finite element simulation techniques and compared with that of the aluminum foam-cored sandwich panel (AFP) of identical dimensions and weight. It has been found that the AXP is far superior to the AFP in ballistic resistance because of the material concentration at the impacted area due to the negative Poisson's ratio (NPR) effect. A parametric study was carried out to investigate the effects of several key parameters, including impact velocity, face and core thicknesses, and core density, on the ballistic resistance of the AXP and AFP. The results show that the ballistic limit and perforation energy of the AXP is greatly affected by these parameters. Meanwhile, the advantages of AXP over AFP being used as ballistic resistant structures are highlighted. The primary outcome of this research is new information on the development and design of advanced ballistic resistant structures containing auxetic materials.