Auxetic metamaterials, known for their unusual properties, are being explored as cores for sandwich structures to improve impact resistance. This study investigated the low-velocity impact response of sandwich panels with various core designs using finite element method (FEM) and experiments on 3D-printed specimens. These cores include pure honeycomb, pure auxetic, and gradient variations with controlled gradients of Poisson’s ratio, transitioning from negative to positive (NTP), positive to negative (PTN), negative-to-positive-to-negative (NTPTN), and positive-to-negative-to-positive (PTNTP). These gradients were achieved by adjusting the unit cell angle within the core. Under quasi-static indentation, the gradient PTN design improved energy absorption by 26% compared to the honeycomb structure, while the gradient NTP structure showed a 9% improvement over the auxetic core. As for the impact tests, the gradient NTP and PTN structures significantly enhanced the indentation resistance of auxetic and honeycomb structures by 21.3% and 6.5%, respectively. Interestingly, while the optimal core for peak energy absorption varied with impact velocity, gradient structures generally provided superior energy absorption, particularly at lower velocities. FEM results at initial impact velocities of 10, 15, 20 m/s confirmed that structures having negative Poisson’s ratio at their top layer exhibited the lowest penetration depth. Additionally, gradient structures, particularly NTP and NTPTN, demonstrated superior energy absorption capability compared to purely auxetic or honeycomb structures, especially at lower velocities. The study highlights the benefits of utilizing gradient auxetic metamaterial cores in high-performance sandwich structures for impact resistance applications. These structures showed minimal localized damage, reduced densification risk due to uniform crushing, and lower penetration depth.