Deterministic switching of polarization vortex in ferroelectrics by a uniaxial mechanical load is challenging. Here, we demonstrate, by using phase field simulations and ferroelectric instability analyses, a deterministic switching of polarization vortex in a compositionally graded ferroelectric (cgFE) nanoplate under a compressive stress. The obtained results suggest that the rational distribution of material constituents in the cgFE nanoplate tailors the distributions of electromechanical coupling and total energy densities of the nanoplate, which modifies the stress-induced vortex multiplication and annihilation behaviours, distinguished from that in a homogeneous ferroelectric nanoplate. The switching of polarization vortex by compressive stress is verified through instability analyses for the cgFE nanoplate, which not only confirm when the polarization switching occurs, but also demonstrate how the polarization responses at the onset of the switching. In addition, the effects of various factors on feasibility of stress-induced vortex switching, including material gradient, temperature, and width-height ratio of the cgFE nanoplate, are investigated and summarized in fruitful phase diagrams.