The cuttlebone structure is a complex porous bionic structure with an asymmetric S-shaped wall structure connecting laminar septa. Studies have shown that the cuttlebone structure has a low weight, high strength, and excellent energy absorption capability. To establish bio-inspired structures with superior biological functions, researchers have proposed the sinusoidally corrugated cuttlebone-like array structure (SCS). In this study, referring to Euler’s theory combined with the Gaussian curvature, the effects of the thickness t, height H, amplitude A, and period P of the SCS under compressive shearing were analyzed. Through finite element calculations and parameter sensitivity analysis, the optimized Su4-Sl2 SCS was obtained. Based on the optimization results, a structure named the elliptical corrugated cuttlebone-like array structure (ECS) was designed. Various ECSs were prepared via three-dimensional (3D) printing, and the compression and shear deformation characteristics of the ECSs were analyzed through experiments and simulations. The results showed that the bearing capacities of the new ECSs were improved compared with those of SCSs; moreover, Eu60-El90, Eu60-El60, and Eu60-El60 ECSs had the best compressive and shear capacities. From the perspective of the stress, the peak compression, peak shear stress in the y-direction, and peak shear stress in the x-direction were increased by 14.2%, 32.8%, and 14.9%, respectively. From the perspective of the energy, the compressive strain energy, shear strain energy in the y-direction, and shear strain energy in the x-direction were increased by 22.8%, 33.0%, and 78.1%, respectively.