In this paper we study a general energy minimization problem for mixed-criticality systems on multi-cores, considering different system operation modes, and static & dynamic energy consumption. While making global scheduling decisions, trade-offs in energy consumption between different modes and also between static and dynamic energy consumption are required. Thus, such a problem is challenging. To this end, we first develop an optimal solution analytically for unicore and a corresponding low-complexity heuristic. Leveraging this, we further propose energy-aware mapping techniques and explore energy savings for multi-cores. To the best of our knowledge, we are the first to investigate mixed-criticality energy minimization in such a general setting. The effectiveness of our approaches in energy reduction is demonstrated through both extensive simulations and a realistic industrial application.