Multi-scale flows are prevalent in extreme flight environments such as planetary reentry, and their inherently multi-scale nature poses severe challenges to traditional numerical methods. To overcome the limitations of conventional CFD and Direct Simulation Monte Carlo (DSMC) methods in cross-regime simulations, specifically the breakdown of the continuum model in the rarefied regime and the severe time-step restriction of particle methods in the continuum regime, various multi-scale numerical methods based on kinetic models were developed in recent years. Among these, the Unified Stochastic Particle (USP) method decomposes the collision term into macroscopic and microscopic parts and solves the transport and collision processes in a coupled manner, thereby circumventing the restrictive temporal and spatial step constraints of the DSMC method and significantly enhancing the accuracy and efficiency of stochastic particle approaches. In this work, the USP method was extend to polyatomic gas mixtures, and the Unified Particle Solver (UniPS) was developed and applied to the numerical simulation of three-dimensional hypersonic multi-scale flows. The solver employed unstructured meshes and a hybrid MPI/OpenMP parallel architecture, with parallelization and memory optimizations implemented for core modules such as particle transport and collision. Numerical validations on two test cases, i.e., a three-dimensional blunt cone and a nozzle vacuum plume, demonstrate that the UniPS solver achieves favorable computational accuracy and parallel efficiency across flow regimes. The USP-DSMC hybrid method shows good agreement with reference solutions in the continuum regime and achieves approximately one order of magnitude speedup over the pure DSMC method under the same accuracy requirement. The MPI/OpenMP hybrid parallelization achieves a parallel efficiency of 64% on 1536 threads. The solver effectively supporting the numerical simulation of hypersonic multi-scale flows.