Auxetic metamaterials exhibit distinctive mechanical properties, such as negative Poisson's ratio, high energy absorption, and enhanced fracture resistance. However, prevailing design methods frequently focus solely on one of these properties under the assumption of small deformation linear elasticity, neglecting the nonlinear mechanical behaviors prevalent in real-world scenarios. To this end, this work proposes a data-driven design approach to customize individually or simultaneously the Poisson’s ratio and compressive modulus undergoes finite compressive strains. Particularly, a baseline metamaterial con-figuration with a prescribed negative Poisson’s ratio is obtained rapidly by nonlinear topology optimization. Subsequently, feature geometry parameters that have the most influence on the target mechanical behaviors are identified with numerical and experimental tests. The identified feature geometry parameters are then used to train a neural network model. With the strongly nonlinear prediction of the trained model, an optimization model employing a genetic algorithm is performed to find a globally optimal Layout characterized by the prescribed Poisson’s ratio and compressive modulus caves. Finally, the proposed method has been shown to possess a customization design capability exceeding 95% through Finite Element Analysis.