The Auxetic Structure (AS) exhibits significant densification strain due to its concave cell architecture, functioning as an effective energy-absorbing metamaterial. However, its limited plateau stress hampers further enhancement of energy absorption. The deep-sea Glass Sponge (GS) has high plateau stress due to its diagonal braces. Inspired by GS, the Glass-Sponge-Auxetic Structure (GSAS) is proposed, featuring concave cells reinforced by diagonal braces to achieve both high plateau stress and densification strain. Different structural configurations incorporating various brace arrangements and thicknesses for GSAS are designed and compared through finite element analysis. An optimal GSAS is achieved with a 0.5 mm strut thickness and an asymmetric arrangement of crossing and uncrossing braces. The GSAS is fabricated using Ti6Al4V through selective laser melting and compared with AS, GS, body-centered cube, and honeycomb in compression tests. The unique bending-stretching deformation and non-simultaneous fracturing pattern results in simultaneous high plateau stress and densification strain, and the highest energy absorption and specific energy absorption. Compared to AS, these values are enhanced by 156% and 75%, respectively. The exceptional energy absorption capability of GSAS presents promising prospects in fields such as automobile collision avoidance and vibration damping, with its customizable cell numbers offering the potential for more specific applications.