The smooth particle hydrodynamics (SPH) method is advantageous in tracking a free surface and a moving interface. This paper uses the SPH method to simulate the filling process of squeeze casting. The simulated temperature field at the end of filling was input into a finite element model (FEM) program to simulate the solidification process after squeeze casting. Due to the existence of a liquid phase, a solid phase, and a two-phase mushy zone in the solidification process after squeeze casting, the deformation behavior in the solidification process was modeled with a thermoelasto–viscoplastic constitutive model representing these different phases. In the RDG thermal cracking criterion based on the principle of dendrite gap complement, there are a strain rate term, a secondary dendritic spacing term, and a pressure term. These terms accurately describe the squeeze casting process. Therefore, the RDG criterion was used to predict thermal cracking. The strain rate term in the RDG criterion was calculated by the FEM. For the calculation of the secondary dendritic spacing, the temperature field during the solidification process is locally refined by the FDM method to complete the transition from the macroscale to the mesoscale; then the refinement results are imported into the phase field method for dendritic growth simulation. The results show that the method based on multi-model coupling has satisfactory prediction accuracy for the thermal cracking in the squeeze casting process. The combination of the phase field method and the RDG criterion provides a new approach to the simulation of thermal cracking defects. The prediction results show that the thermal cracking tendency increases with an increase in strain rate. However, the local position C of the bracket sample had a higher strain rate of 7.15/s, and a lower cooling rate of 2.96 K/s offset the effect of the high strain rate. As a result, a low thermal cracking tendency level of 1.13729 was obtained.