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Na3+yV2-yMgy(PO4)3 (0 ≤ y ≤ 1) NASICON compounds, thanks to their relative simplicity and the presence of a single redox-active species, are of interest for understanding the function and limitations of more complex, mixed transition metal NASICON-type Na-ion cathodes. Partial Mg substitution for V in Na3+yV2-yMgy(PO4)3 leads to a gradual transition from a two-phase to a solid solution Na (de)intercalation mechanism during electrochemical cycling. When cycled over a narrow voltage window (3.8 – 2.75 V vs. Na+/Na0), these cathodes exhibit good structural and electrochemical reversibility, leading to a high capacity retention. Yet, when the upper cutoff voltage is increased from 3.8 V to 4.2 V, significant irreversibilities arise, accompanied by a notable evolution of the electrochemical profiles during the first cycle. We focus here on the y = 0.5 and 1 compounds and use a combination of electrochemical testing, advanced characterization, and first principles density functional theory calculations to investigate the redox and structural processes taking place at high potentials. In-situ and ex-situ X-ray diffraction, and 23Na and 31P solid-state NMR reveal bulk structural rearrangements, at least partly caused by Na extraction from Na(1) sites. For the y = 1 cathode, an irreversible phase transition leads to a change in the symmetry of the crystal structure from rhombohedral to monoclinic. For both compounds, substantial distortions of the VO6 octahedra and irreversible changes to the local structure are observed using X-ray absorption spectroscopy during high voltage cycling, but our 51V NMR results show no evidence for V migration. Instead, first principles nudged elastic band calculations suggest low energy migration pathways for Mg2+ into vacant face-sharing Na(1) sites at high states of charge. These findings are consistent with the significant evolution of the electrochemical profile during the first cycle, voltage hysteresis, and subsequent rapid capacity decay. More broadly, these results could suggest similar structural rearrangements (e.g., Mn migration) in related V- and Mn-containing NASICON cathodes, which also show poor reversibility when cycled up to high potentials.