This paper investigates the deformation mechanism and energy absorption behaviour of 316 L triply periodic minimal surface (TPMS) structures with uniform and graded wall thicknesses fabricated by the selective laser melting technique. The uniform P-surface TPMS structure presents a single-level stress plateau for energy absorption and a localized diagonal shear cell failure. A graded strategy was employed to break such localized geometrical deformation to improve the overall energy absorption and to provide a double-level function. Two segments with different wall thicknesses separated by a barrier layer were designed along the compression direction while keeping the same relative density as the uniform structure. The results show that the crushing of the cells of the graded P-surface TPMS structure occurs first within the thin segment and then propagates to the thick segment. The stress–strain response shows apparent double stress plateaus. The stress level and length of each plateau can be adjusted by changing the wall thickness and position of the barrier layer between the two segments. The total energy absorption of the gradient TPMS structure was also found slightly higher than that of the uniform TPMS counterparts. The gradient design of TPMS structures may find applications where the energy absorption requires a double-level feature or a warning function.