The phase transition (PT) in phase change materials (PCMs) can be triggered by external stimuli, e.g., light or heat, resulting in a drastic change in their physical properties, such as electrical resistivity. Due to this rapid PT, PCMs are promising candidates for various applications, including reconfigurable electronics, photonics, sensors, and memory devices. Here, a coupled phase-field model was developed to investigate the effect of mechanical stress as an overlooked factor on the PT of germanium–antimony–tellurium. The results suggest that mean compressive stress promotes crystal growth, while tensile stress hinders crystallization. Moreover, stress alters the shape of spherical nuclei and promotes the anisotropic growth. Finally, mushroom-shaped grains can be formed in the high-temperature regime due to the heterogeneous stress distribution around interacting nuclei. These findings suggest a pathway for tailoring microstructure and tuning/controlling crystallization time via mechanical stresses.