A non-steady state mathematical model of an amino acid (phenylalanine (Phe)) and mineral salt (NaCl) solution separation by neutralization dialysis (ND) carried out in a batch mode is proposed. The model takes into account the characteristics of membranes (thickness, ion-exchange capacity, and conductivity) and solutions (concentration, composition). As compared to previously developed models, the new one considers the local equilibrium of Phe protolysis reactions in solutions and membranes and the transport of all the phenylalanine forms (zwitterionic, positively and negatively charged) through membranes. A series of experiments on ND demineralization of the NaCl and Phe mixed solution was carried out. In order to minimize Phe losses, the solution pH in the desalination compartment was controlled by changing the concentrations of the solutions in the acid and alkali compartments of the ND cell. The validity of the model was verified by comparison of simulated and experimental time dependencies of solution electrical conductivity and pH, as well as the concentration of Na+, Cl−ions, and Phe species in the desalination compartment. Based on the simulation results, the role of Phe transport mechanisms in the losses of this amino acid during ND was discussed. In the experiments carried out, the demineralization rate reached 90%, accompanied by minimal Phe losses of about 16%. Modeling predicts a steep increase in Phe losses when the demineralization rate is higher than 95%. Nevertheless, simulations show that it is possible to achieve a highly demineralized solution (by 99.9%) with Phe losses amounting to 42%.