Stochastic, spatial reaction-diffusion simulations have been widely used in systems biology and computational neuroscience. However, the increasing scale and complexity of simulated models and morphologies have exceeded the capacity of any serial implementation. This led to development of parallel solutions that benefit from the boost in performance of modern large-scale supercomputers. In this paper, we describe an MPI-based, parallel Operator-Splitting implementation for stochastic spatial reaction-diffusion simulations with irregular tetrahedral meshes. The performance of our implementation is first examined and analyzed with simulations of a simple model. We then demonstrate its usage in real-world research by simulating the reaction-diffusion components of a published calcium burst model in both Purkinje neuron sub-branch and full dendrite morphologies. Simulation results indicate that our implementation is capable of achieving super-linear speedup for balanced loading simulations with reasonable molecule density and mesh quality. In the best scenario a parallel simulation with 2000 processes achieves more than 3600 times of speedup relative to its serial SSA counterpart and more than 20 times of speedup relative to parallel simulation with 100 processes. While simulation performance is affected by unbalanced loading, a substantial speedup can still be observed without any special treatment.