Vortex domain patterns in low-dimensional ferroelectrics and multiferroics have been extensively studied with the aim of developing nanoscale functional devices. However, control of the vortex domain structure has not been investigated systematically. Taking into account effects of inhomogeneous electromechanical fields, ambient temperature, surface and size, we demonstrate significant influence of mechanical load on the vortex domain structure in ferroelectric nanoplatelets. Our analysis shows that the size and number of dipole vortices can be controlled by mechanical load, and yields rich temperature-stress (T-S) phase diagrams. Simulations also reveal that transformations between "vortex states" induced by the mechanical load are possible, which is totally different from the conventional way controlled on the vortex domain by the electric field. These results are relevant to application of vortex domain structures in ferroelectric nanodevices, and suggest a novel route to applications including memories, mechanical sensors and transducers.