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Recent works introduce a semi-clairvoyant model, in which the system mode transition is revealed on the arrival of high criticality jobs. To solve the problem of inconsistency between the correctness criterion for mixed-criticality systems (MCS) with a semi-clairvoyant and the actual situation, we study the problem of schedulability and energy in MCS with the semi-clairvoyant model in this paper. First, we propose a new correctness criterion for MCS with semi-clairvoyant and graceful degradation and develop the schedulability test based on Demand Bound Function methods denoted as SCS-GD. Second, we propose an energy-efficient semi-clairvoyant scheduling algorithm based on SCS-GD denoted as EE-SCS-GD. Finally, we conduct an experimental evaluation of SCS-GD and EE-SCS-GD by synthetically generated task sets. The experimental results show that SCS-GD can improve the schedulability ratio by 5.98% compared to existing algorithms while EE-SCS-GD can save 56.17% energy compared to SCS-GD.