Embedded systems are getting into various domains of our daily life as well as in many of the highly sophisticated large systems, such as air planes, military tanks, rockets, satellites. These large systems consist of many modules which are executing umpteen number of tasks semi-independently. However, not all tasks have the same levels of priority and/or criticality. One way is to design individual systems with dedicated processors to avoid the dependency as proposed by the industry. However, mixed-criticality notion helps to enhance system performance, and reduce system cost, size, and weight. The idea is to integrate functionalities of different safety criticality levels into a common computing platform. Further, the energy consumption of these systems should also be taken into account. While there are many algorithms under the broad umbrella of scheduling - preemptive, non-preemptive, etc., -- solutions that jointly minimizes both static and dynamic energy consumption in mixed-criticality systems on multi-cores under partitioned scheduling are, hitherto, not addressed in depth. To reconcile the conflicting requirements of safety and energy: (i) we formulate a general energy minimization problem; (ii) we provide an analytical optimal solution on unicore systems and a corresponding low-complexity heuristic and (iii) we provide energy-aware mapping techniques based on our unicore solutions on multi-cores. Effectiveness in energy reduction is demonstrated for our solutions through extensive simulations with synthetic task sets.