Schwarzites are 3D crystalline porous materials exhibiting the shape of Triply Periodic Minimal Surfaces (TPMS). They possess negative Gaussian curvature, created by the presence of rings with more than six sp2-hybridized carbon atoms. Recently, new routes to their synthesis have been proposed. Due to its foam-like structure, schwarzites are interesting for mechanical energy absorption applications. In this work, we investigate through fully atomistic reactive molecular dynamics the mechanical response under ballistic impacts of four structures from primitive (P) and gyroid (G) families (two structures within each family). The two structures in the same family differ mainly by the ratio of hexagons to octagons, where this ratio increases the flatness of the structures. Although the penetration depth values are higher in the flatter structures (P8bal and G8bal), the absorbed kinetic energy by them is considerably higher, which yields them a better energy-absorption performance.