<p>The auxetic structure has garnered significant attention due to its unique negative Poisson’s ratio effect and exceptional mechanical properties. To further improve the stiffness and energy absorption capacity of the structure, this paper proposes a modified re-entrant auxetic honeycomb structure by introducing a circular structure into a re-entrant hexagonal honeycomb cell and then connecting the two together using two reinforcing bars. The bending performance of their made sandwich beams (MRBs) is investigated by the finite element method. The results show that the MRB preserves the negative Poisson's ratio characteristics of the RB compared to the re-entrant hexagonal honeycomb sandwich beam (RB). In addition, the maximum compressive force and specific energy absorption of the MRB, respectively, increase by 232.8 and 111.8%, which significantly improves its stiffness and energy absorption performance. Subsequently, the parameter analysis revealed that the stiffness, energy absorption, and auxetic effects of the MRB can be further optimized by properly adjusting the geometric parameters. Finally, the complex proportionality assessment method (COPRAS) is implemented to determine the influence weights of the structural parameters on the bending performance of the sandwich beams. The results show that the structural parameters of the core layer have a more significant effect on the bending performance, especially with the modified honeycomb cell thickness. This study provides new insights into optimizing auxetic structure design in terms of stiffness, energy absorption, and auxetic effects.</p>