Auxetic material is a metamaterial engineered to achieve negative Poisson's ratios through special design of microstructure. As a typical 3D auxetic material, 3D cross-chiral structures (CCS) possesses significant auxetic behavior and the mechanical properties can be tuned over a wide range. In this paper, mechanical responses of CCS are systematically investigated by experiments, numerical simulations and theoretical analysis. Three typical failure modes are observed during the compression process. As the tilt angle of struts increases, the CCS shows a transition from the compression-dominated to the bending-dominated deformation mechanism. The Young's modulus of the CCS can be enhanced 8.5 times, simply by changing the angle of the strut by 20°. The CCS can also show a higher energy absorption capacity with absorption efficiency of about 50%, which is higher than most previously reported cellular materials. Additionally, a new theoretical model based on large deformation theory is established to predict the plastic yield stress, and good agreement is obtained with the numerical simulations and experiments, which indicates that the present model can significantly improve the accuracy of the estimation. The results of this paper may be helpful for designing of energy absorbing devices and personal protection with 3D auxetic materials. Display omitted •Three typical failure modes of the CCS observed in both experiments and simulations are controlled by the configuration.•CCS shows a transition from the compression-dominated to the bending-dominated in deformation mechanisms as q increases.•CCS shows absorption efficiency of about 50%, which is higher than most previously reported cellular materials.•Based on large deformation theory, the theoretical model could present more accurate predictions of plastic yield stress.