Sodium manganese hexacyanomanganate, NaxMn[Mn(CN)6], is an electrochemically active Prussian blue analog (PBA) that has been studied experimentally as an electrode material in rechargeable sodium-ion batteries. It has a reversible specific capacity of 209 mAh/g, which is substantially higher than the theoretical specific capacity of 172 mAh/g expected for two reduction events conventional in the PBAs. It has been suggested the high specific capacity originates from this compound's unique ability to insert a third sodium ion per formula unit. However, the plausibility of this mechanism has remained ambiguous. Here we use density-functional theory (DFT) with a hybrid functional to calculate the formation energies of various oxidation states and magnetic phases of the NaxMn[Mn(CN)6] system. We confirm that the compound Na3Mn(II)[Mn(I)(CN)6] is, indeed, thermodynamically stable. It contains manganese(I) and the sodium ions occupy the interfacial position of the lattice subcubes. We also provide strong evidence that the phase of the fully oxidized Mn[Mn(CN)6] compound is charge-disproportionated, containing manganese(II) and manganese(IV). We proceed to show that the presence of crystalline water increases the reduction potential of the system and that the hydrated compounds have theoretical crystal geometries and reduction potentials that closely match experiment. This work clarifies the charge-storage mechanism in a well-known but less-understood PBA.