The scheduling of mixed-criticality (MC) systems with graceful degradation is considered, where LO-criticality tasks are guaranteed some service in HI mode in the form of minimum cumulative completion rates. First, we present an easy to implement admission-control procedure to determine which LO-criticality jobs to complete in HI mode. Then, we propose a demand-bound-function-based MC schedulability test that runs in pseudo-polynomial time for such systems under EDF-VD scheduling, wherein two virtual deadline setting heuristics are considered. Furthermore, we discuss a mechanism for the system to switch back from HI to LO mode and quantify the maximum time duration such recovery process would take. Finally, we show the effectiveness of our proposed method by experimental evaluation in comparison to state-of-the-art MC schedulers.