The microstructure and material properties of auxetic honeycomb metamaterials significantly influence their deformation behavior and energy absorption. Inspired by the arch bridge, new types of straight-arc coupled structure (SACS) and the reverse SACS (R-SACS) auxetic metamaterials are designed to enhance the energy absorption capacity (EAC). The quasi-static compression and dynamic impact responses of honeycomb metamaterials are studied numerically under large deformation. A theoretical model is further developed to estimate the average platform stress (σp) of the R-SACS honeycomb, which is verified by the numerical results. For R-SACS--3 with Nylon 12 and Al-alloy, the relative errors of the finite element model compared with the theoretical model are − 5.56 % and − 3.21 %, respectively. Two kinds of basic materials, Nylon 12 and Al-alloy, are employed to analyze the deformation mode of the SACS and R-SACS honeycomb with the same geometric parameters under quasi-static load and impact load. The influence of basic material is discussed, and the structure with Al-alloy exhibits more stability owing to segmented deformation. The creation of additional plastic angles shows an improved σp and specific energy absorption (SEA) compared to the re-entrant structure (RES). σp and SEA of SACS are both 1.3 times as much as those of RES. The peak stress of the R-SACS cellular metamaterial is always smaller than the SACS under impact load, and the maximum reduction is 63 %, which has better a buffering effect.