The development of additive manufacturing and lattice structures has created opportunities for the development of lightweight impact–absorption structures that can overcome most constraints of previously used materials such as expanded polystyrene foams. However, for the successful application of such structures, the effects of their variables in their mechanical performance must be established. In this study, the mechanical properties and energy absorption of thermoplastic sheet gyroid structures were investigated and compared with the performance of current materials. Consequently, the specimens were tested after changing the main variables, i.e., cell size and volume fraction, of various thermoplastic materials such as acrylonitrile butadiene styrene, polylactic acid, thermoplastic polyurethane, and polyamide 12. Finally, they were tested in a quasi-static compression test and their deformation stages were photographed. The stress–strain curves of all materials changed after adopting the sheet gyroid structure, exhibiting three distinct regions: linear elastic, long collapse plateau, and densification that made them particularly applicable for energy absorption. Volume fraction affected the layer collapse. The elastic geometrical stiffness increased for higher volume fractions and smaller cells. In addition, the peak and plateau stresses increased at higher volume fractions, and while smaller cells were not directly affected. Additionally, the area under the curves increase with the volume fraction; hence, for most materials, specific energy absorption was larger for higher volume fractions. The constituent material properties contributed significantly to the structural behavior, exhibiting three primary deformation mechanisms, i.e., elastomeric, elastic–plastic, and elastic–brittle, resulting in a wide spectrum of properties for each application requirement. The comparison of the optimal properties with the expanded polystyrene demonstrated the ability of sheet gyroid structures to overcome most of its challenges, exhibiting a superior specific energy absorption, ability to withstand various impacts, letting air flow in its all axes, and being recyclable. Thus, sheet gyroid structures can be considered promising alternatives.