The realization of the axion insulator phase in magnetic topological insulators is often hindered by crystalline symmetries that protect gapless surface states, even when time-reversal symmetry is broken. Here, we use variable-temperature scanning tunneling microscopy (STM) and spectroscopy (STS), complemented with density functional theory (DFT), to investigate the local electronic structure of the antiferromagnetic (AFM) topological insulator EuSn₂As₂ across its Néel transition at T_N = 24 K. On the (001) surface, we observe a substantial density of intrinsic Sn vacancies that introduce nanoscale electronic inhomogeneity and p-type doping. Upon cooling below T_N, we resolve the emergence of two distinct magnetically driven gaps: a ∼100 meV gap near the Fermi level and a ∼50 meV gap at the ARPES-resolved Dirac point. We attribute the former gap to AFM Brillouin-zone folding and hybridization. The characteristics of the 50 meV gap point toward the lifting of mirror-symmetry protection by Sn vacancies and the consequent mass gapping of the Dirac point, although contributions from AFM-induced folding hybridization cannot be entirely ruled out. Our findings provide real-space evidence for strong coupling between localized moments and itinerant topological states, highlighting exfoliable EuSn₂As₂ as a potential candidate for realizing axion-insulator-based devices.