A personalized, 3D printed, multi-material artificial spinal disc is expected to not only achieve personalized anatomical fit, but also to restore the natural mechanics of the implanted spinal segment. However, the necessary structure for disc design is not explored and optimizing the design is challenging due to the high-dimensional search space provided by the material distribution precision of multi-material 3D printing as well as necessary nonlinear finite element simulation. Therefore, this study explores the feasibility of two multi-material spinal disc designs and a clustering-based design variable linking method to achieve efficient and effective optimization. The optimization goal is to enable the implant to have natural stiffnesses for five loading cases. The results show that a biomimetic fiber network is necessary for the disc design. Moreover, the optimization performance of the heuristic derived from a clustering-based method is shown to be a good trade-off between the objective function value and the computational time.