Magnesium aluminate spinel (MgAl2O4), like many other ceramic materials, offers a range of technological applications, from nuclear reactor materials to military body armor. For many of these applications, it is critical to understand both the formation and evolution of lattice defects throughout the lifetime of the material. We use the Speculatively Parallel Temperature Accelerated Dynamics (SpecTAD) method to investigate the effects of di-vacancy and di-interstitial formation on the mobility of the component defects. From long-time trajectories of the state-to-state dynamics, we characterize the migration pathways of defect clusters, and calculate their self-diffusion constants across a range of temperatures. We find that the clustering of Al and O vacancies drastically reduces the mobility of both defects, while the clustering of Mg and O vacancies completely immobilizes them. For interstitials, we find that the clustering of Mg and O defects greatly reduces O interstitial mobility, but has only a weak effect on Mg. These findings illuminate important new details regarding defect kinetics relevant to the application of MgAl2O4 in extreme environments.