Mixed cation mixed halide perovskites (MHPs) are promising candidate materials for next-generation photovoltaic devices due to their remarkable optoelectronic properties and tunable bandgaps. However, their performance can be significantly affected by the phase segregation of anions that occurs due to ion migration in the lattice. In this study, we investigate the effects of external pressure on the phase segregation behavior of mixed bromide/iodide perovskites through first-principles-based simulations. By subjecting the perovskite lattice to varying pressures, we explore the modifications in the local structure that significantly impact the ion dynamics within the perovskite lattice. We analyze the energetics associated with defect formation and barriers for migrating halide ions under compressive stress. Our results reveal that compressed lattice prefers defect-assisted random hopping of bromide and iodide ions along equatorial planes, indicating suppressed phase segregation. The local lattice distortion under pressure can also substantially reduce the anion diffusion along the axial plane. These computational insights would immensely help to strategically design and postprocess halide perovskites with longterm operational stability, arising due to largely suppressed ion dynamics.