Conventional positive Poisson’s ratio honeycombs are prone to stress concentration and premature collapse under impact loading. Auxetic structures can reduce this problem through inward transverse deformation, but the coupled effect of auxetic geometry and nano-reinforced polymer matrices on impact energy absorption remains insufficiently understood. In this study, pure PLA and 1 wt% graphene nanoplatelet (GNP)/PLA filaments were prepared by solution blending and twin-screw extrusion, and double-arrow negative Poisson’s ratio (NPR) honeycombs with upper-arm angles from 40° to 80° were fabricated by fused deposition modeling. Drop-weight impact tests and finite element simulations were conducted to examine the geometry-dependent crashworthiness response. Among the tested configurations, the θ1 = 50° GNP/PLA structure reached a specific energy absorption of 3.12 J/g and a crashworthiness efficiency of 0.69, giving the best balance between energy absorption and load stability in this study. Compared with the corresponding PLA structures, the GNP/PLA structures showed higher impact-resistance metrics across the tested geometries. The increase in SEA was greater than the material-level tensile improvements, indicating that matrix reinforcement can be more effectively translated into structural energy absorption when the collapse mode is appropriately tuned. These results show that low-content GNP reinforcement and angle-tuned double-arrow NPR geometry can work together to improve the impact energy absorption of FDM-printed PLA metamaterials within the tested design space.