In this paper, the problem of finding the optimal separation sequence for a three-component mixture in a cascade of two binary separation stages is considered. The minimal energy that is needed for a separation in a two-stage mechanical separation subject to a given flow rate of the input mixture is obtained. Optimization is achieved by selecting the optimal sequence of binary separations and by distributing mass-exchange surfaces between separation stages optimally. For a heat-driven two-stage separation system, it is shown that the rate of flow of the input mixture cannot be higher than some bound. This bound (the maximal possible rate of heat-driven separation) and the separation sequence when it is achieved are derived.