We introduce a computational approach to optimize random porous materials through parametric growth processes. We focus on the particular problem of minimizing the Poisson's ratio of a two-phase porous random material, which results in an auxetic material. Initially, we perform a parametric optimization of the growth process. Afterward, the optimized growth process is used to directly generate an auxetic random material. Namely, the growth process intrinsically entails the formation of an auxetic material. Our approach enables the computation of large-scale auxetic random materials in commodity computers. We also provide numerical results indicating that the computed auxetic materials have close to isotropic linear elastic behavior.