We propose a new concept that utilizes the difference in Poisson's ratio between component materials as a strengthening mechanism that increases the effectiveness of the sacrificial bond toughening mechanism in macroscale double-network (Macro-DN) materials. These Macro-DN composites consist of a macroscopic skeleton imbedded within a soft elastic matrix. We varied the Poisson's ratio of the reinforcing skeleton by introducing auxetic or honeycomb functional structures that results in Poisson's ratio mismatch between the skeleton and matrix. During uniaxial tensile experiments, high strength and toughness were achieved due to two events: (1) multiple internal bond fractures of the skeleton (like sacrificial bonds in classic DN gels) and (2) significant, biaxial deformation of the matrix imposed by the functional skeleton. The Macro-DN composite with auxetic skeleton exhibits up to 4.2 times higher stiffness and 4.4 times higher yield force than the sum of the component materials. The significant improvement in mechanical performance is correlated to the large mismatch in Poisson's ratio between component materials, and the enhancement is especially noticeable in the low-stretch regime. The strengthening mechanism reported here based on Poisson's ratio mismatch can be widely used for soft materials regardless of chemical composition and will improve the mechanical properties of elastomer and hydrogel systems.