Due to their exceptional lightweight and mechanical properties, triply periodic minimal surface (TPMS) based lattice structures have been widely studied. In this paper, the energy absorption performance of eight TPMS structures under large deformation was thoroughly studied, and five meshing strategies were evaluated comprehensively for the first time. The research objectives include three parts. First, the mechanical properties of eight TPMS structures, namely Primitive (P), Gyroid (G), Diamond (D), I-Wrapped Package (I-WP), Fischer-Kock (F-K), Neovius (N), I₂-Y^⁎⁎ and F-Rhombic Dodecahedra (F-RD) lattices, were investigated by utilizing experimental and numerical methods. These TPMS structures were fabricated using 316L stainless steel powder by selective laser melting (SLM) and compared experimentally under compression in terms of the stress-strain curve, deformation and energy absorption. The results showed that F-RD and D lattice structures exhibit the best energy absorption capacity at relative densities less and greater than 30%, respectively. Second, to evaluate different meshing strategies for these complex structures, five finite elements (FE) models based on the shell, solid, and voxel elements were compared in terms of modeling ease, computational efficiency, data management, and simulation accuracy. It was demonstrated that the quadrilateral shell model shows satisfactory results for lattice structures with low relative densities or thin walls. In contrast, the voxel model shows the best results for structures with higher relative densities or thicker walls. Last, the voxel model was applied to the F-RD and D lattice structures. The numerical results showed that the stress distribution was more uniform in the F-RD, and the internal self-contact occurred later in the D lattice structure, further confirming the experimental observation and revealing the energy absorption mechanisms of TPMS structures.