The electrochemical degradation of two solvent-based electrolytes for Mg-metal batteries is investigated through a grand canonical density functional theory (DFT) approach. Both electrolytes are highly reactive in the double layer region where the solvated species have no direct contact with the Mg-surface, hence emphasizing that surface reactions are not the only phenomena responsible for electrolyte degradation. Applied to dimethoxyethane (DME) and ethylene carbonate (EC), the present methodology shows that both solvents should thermodynamically decompose in the double layer prior to the Mg2+/Mg-0 reduction, leading to electrochemically inactive reaction products. Based on thermodynamic considerations, Mg-0 deposition should not be possible, which contrasts with experiments, at least for DME-based electrolytes. This apparent contradiction is here addressed through the rationalization of the electrochemical mechanism underlying solvent electroactivation. An extended operation potential window (OPW) is extracted, in which the Mg2+/Mg-0 reduction can compete with electrolyte decomposition, thus enabling battery operation beyond the solvated species thermodynamic stability. The chemical study of the degradation products is in excellent agreement with experiments and offers rationale for the Mg-battery failure in EC electrolyte and capacity fade in DME electrolyte. The potential-dependent approach proposed herein is thus able to successfully tackle the challenging problem of interface electrochemistry. Being fully transferable to any other electrochemical systems, this methodology should provide rational guidelines for the development of viable electrolytes for multivalent batteries and, more generally, energy conversion and storage devices.