Triply periodical minimal surface (TPMS) structures have attracted much attention in the biomaterials, aerospace, and automotive industries because they are lightweight, have high strength, and can absorb energy and shocks. In this study, uniform skeletal (USK), uniform sheet (USH), grade skeletal (GSK), and grade sheet (GSH) diamond lattice structures with the same 20% volume fraction were fabricated by selective laser melting (SLM) using AlSi10Mg metal powder. Their mechanical properties, deformation behavior, and energy absorption performance were systematically investigated by compression tests and finite element analysis (FEA). The skeleton structures had a higher elastic modulus, yield strength, and more severe stress fluctuation than the sheet structures. In addition, comparing the 45° shear deformation for as-built uniform structures accompanied by a mixture of ductile and brittle fracture modes, both gradient structures fractured by a sub-layer pattern from the layer with a lower volume fraction. Furthermore, the numerical simulation results illustrated that the stress of the skeleton structures was mainly concentrated at the skeleton joint, while the sheet structures were distributed evenly on the thin wall, without being concentrated in the interconnection region. For skeleton structures, heat treatment controlled the failure degree by improving the microstructure of the material, while for GSH structures at 300 °C, the fracture mode changed from the previous layer-by-layer fracture to a 45° shear failure. The accumulated energy absorption of gradient structures was more than that of the uniform structure, especially the GSH structures and the energy absorption efficiency of the skeleton structures was higher.