Industrial Internet of Things (IIoT) provide a promising opportunity for building efficient industrial wireless systems by leveraging the growing ubiquity of sensor nodes. However, IIoT exhibits strict reliability and has a high requirement for real-time communications. Furthermore, different criticality level flows are coexisted in many IIoT. The system must guarantee the reliability and real-time performance of high-criticality flows to avoid disasters. To address this issue, this paper first proposes a heterogeneous routing model in which both source and graph routing coexist. Then, we propose Relative-execution Deadline First (RDF) scheduling and prove it has a better performance than the fixed priority (FP) and earliest deadline first (EDF) methods. By extending RDF in mixed-criticality IIoT, a Mixed-Criticality Relative-execution Deadline scheduling algorithm (MCRD) has proposed, which can further improve system schedulability by making a trade-off between reliability and real-time performance. Simulation and experiment results show that our approach outperforms the existing methods.