The low-energy and low-cost process development and design has always been a hot topic and challenge in separating azeotropic systems in the world. In this paper, a novel, energy-saving reactive pressure-swing distillation (RPSD) was, for the first time, designed for separating the ternary mixture of tetrahydrofuran (THF)-methanol–water. In the reactive distillation column, the process of reacting water with ethylene oxide to produce ethylene glycol for the first time was used to separate THF-methanol–water mixture, then the residual mixtures were separated by two pressure-swing distillation columns. Two feasible RPSD separation processes were investigated in terms of thermodynamic modeling and T-xy phase diagram analysis to achieve optimal separation sequence. The two designed separation processes were optimized by a multi-objective genetic algorithm and heat integration to maximize economic benefit. Results demonstrated that, compared to the conventional pressure-swing distillation process, the total annual cost of the designed two heat-integrated processes based on the RPSD-B process were greatly reduced, i.e., 45.9% and 52.2%, respectively. This paper has important guiding significance for the separation and purification of multicomponent azeotropes.