According to the conventional mixed-criticality (MC) system model, low-criticality tasks are completely discarded in high-criticality system mode. Allowing such loss of low-criticality tasks is controversial and not obviously necessary. We study how to achieve graceful degradation of low-criticality tasks by continuing their executions with imprecise computing or even precise computing if there is sufficient utilization slack. Schedulability conditions under this Variable-Precision Mixed-Criticality (VPMC) system model are investigated for partitioned scheduling and fpEDF-VD scheduling. It is found that the two scheduling methods in VMPC retain the same speedup factors as in conventional MC systems. We develop a precision optimization approach that maximizes precise computing of low-criticality tasks through 0-1 knapsack formulation. Experiments are performed through both software simulations and Linux prototyping with consideration of overhead. The results show that schedulability degradation caused by continuing low-criticality task execution is often very small. The proposed precision optimization can largely reduce computing errors compared to constantly executing low-criticality tasks with imprecise computing in high-criticality mode. The prototyping results indicate that partitioned scheduling in VPMC outperforms the latest work based on fluid model.