Cellular materials, such as lattices and honeycombs, were widely used for structural protection owing to their excellent mechanical properties. By combining the excellent characteristics of lattice and honeycomb curved surface structures, this study designed a cell called Cubic Spherical Hollow (CSH), which had the advantages of orthogonal isotropy and better spatial connectivity. Inspired by the micro-structural arrangement of bamboo fiber and conch shell, we designed the new CSH cellular materials through the interlayer offset strategy. Then, the effects of interlayer offset on the mechanical properties and compression deformation behavior were explored experimentally and simulatively. Compared with other cellular materials, CSH cellular materials exhibited excellent mechanical properties with higher specific strength and specific modulus. The arrangement offsets of the CSH cells between different layers led to a change in the deformation mechanism from a rod’s compressive mode to a combination of a rod’s compressive mode and curved surface’s bending mode. The initial peak stress and plateau stress decreased with the increased arrangement offsets of the CSH since the extruded protrusions of the structure filled the holes and reduced the lateral expansion behavior of the material in the pressurized environment. This phenomenon also reduced the transverse expansion and prevented the sudden change in stress in the constrained space, indicating that the structural deformation was stable and had excellent cushioning and energy absorption properties. In this study, the cellular material design strategy opens a new avenue for energy absorption.