Mechanical metamaterials are typically designed through periodic replication of specially engineered unit cells, yet the efficiency and adaptability of many natural materials arise from structural disorder. This contrast suggests that randomness may serve as a promising design principle for functionalities inaccessible in perfectly ordered architectures. Here, we investigate the tunability of elasticity and Poisson’s ratio in two-dimensional stress-free spring networks with controlled disorder. We identify a structural crossover in which Delaunay-triangulation violations coincide with enhanced elastic heterogeneity. Motivated by this observation, we introduce bond-flipping disorder as a physics-inspired strategy to directly disrupt Delaunay triangulation, bypassing the need for computational optimization or large geometric distortions. This mechanism enables programmable elasticity and robust auxeticity by promoting non-affine deformations. By systematically combining lattice distortion and bond flipping, we delineate the parameter space for negative Poisson’s ratio and demonstrate the universality of disorder-induced auxeticity. Our results establish a framework for designing programmable, isotropic metamaterials with tunable elasticity based on structural disorder.