A coupled separation system involving a mechanical vapor recompression heat pump (MVRHP) and double-effect distillation (MED) was proposed. In a case of separating N,N-dimethylacetamide (DMAC)/water mixture, four distillation schemes (i.e., conventional distillation, top MVRHP distillation, double-effect distillation, and double-effect distillation with double MVRHP) were conceptually constructed and simulated by using Aspen Plus with the binary interaction parameters of the NRTL thermodynamic model. We evaluated these four schemes to choose the best one with the goal of the minimum total annual cost (TAC). Compared to the conventional distillation, the TACs for double-effect distillation with double MVRHPs, top MVRHP distillation, and double-effect distillation were decreased by 47.76, 32.23, and 5.45%, respectively. It indicates that the double-effect distillation with double MVRHPs has obvious advantages over the other three distillation schemes in terms of economic efficiency.