Abstract Sandwich structures are known for their exceptional mechanical properties and widespread applications. This study integrates additive manufacturing (AM) technology, experiments, theoretical equations, and numerical simulations to investigate a novel lightweight sandwich structure with a core based on Triply Periodic Minimal Surfaces (TPMS). The core incorporates Primitive, Neovius, and Diamond structures and is designed and manufactured using AM. Three‐point bending experiments are conducted to assess bending performance, failure modes, and energy absorption capability. A numerical model is established to analyze behavior under bending loads, validated through comparison with theoretical equations and numerical simulations, focusing on stress concentration areas. A parametric study investigates the effects of skin material, thickness, and TPMS core relative density on bending performance and energy absorption capacity. Furthermore, a functionally graded core layer with a gradient change in relative density is designed to study its influence on bending performance. The parameters of the core have a decisive impact on TPMS sandwich panel performance. This study demonstrates that sandwich structures with TPMS cores can be designed to possess desirable bending performance and energy absorption capacity, providing insights for future engineering applications. Highlights A novel TPMS sandwich structure is fabricated using 3D printing technology. The gradient relative density core is introduced. The bending performance and failure behavior of the structure are evaluated. A parametric study was conducted to investigate the effects on performance.