Magnetization is one of the most significant challenges for the application of bulk superconductors. During the pulsed field magnetization process, large numbers of quantized magnetic flux vortices can rush in or out of the superconducting sample, which generates a significant amount of heat and can lead to the thermomagnetic instability of the bulk superconductor. The large Lorentz force and the sharp temperature rise can result in mechanical failure (or instability), which also hinders the application of bulk superconductor. In addition, thermomagnetic instability and mechanical failure may couple with each other. Thus, it is challenging to simulate the magnetization of bulk superconductors used as high field magnets. In this paper, a numerical simulation framework based on the coupled H-formulation for the electromagnetic behavior of superconductors, the heat diffusion equation, and the phase-field model for the failure of solids is proposed and implemented to simulate the thermal-magnetic-mechanical instability behavior of bulk superconductors during the magnetization process. The thermal-magnetic-mechanical instability-induced dendritic flux patterns are obtained and the corresponding material damage are evaluated through these numerical simulations. The magnetic field, current density, temperature, stress/strain field distribution, and the material failure within the bulk sample in the high magnetic field magnetization process will also be presented.