Auxetic structures possess negative Poisson’s ratio (NPR). They exhibit enhanced indentation resistance, synclastic deformation, high fracture toughness and high energy absorption. Several sorts of auxetic structures exist, such as re-entrant, arrowhead, chiral, etc. The re-entrant structure is the most common sort of auxetic structures. This paper investigates the mechanical behavior of the re-entrant auxetic structure using experimental and numerical methods. Two modified re-entrant topologies are proposed based on the original (conventional) re-entrant topology. Using these modified topologies, two re-entrant auxetic sandwich structures are designed and 3D printed using fused deposition modeling (FDM) out of polylactic acid (PLA). Conducting compression, three and four-point bending tests, the compressive and flexural performance of the two new re-entrant auxetic sandwich structures is studied and compared with the original (conventional) re-entrant structure. More specifically, Poisson’s ratio, compressive modulus, flexural stiffness and maximum loads of the structures are focused and studied. The mechanical properties of auxetic sandwich structures are improved using modified topologies. The new re-entrant auxetic sandwich structures show 11% higher normalized compressive modulus and 9% higher normalized flexural stiffness than the original re-entrant structure.