Mixed-Criticality Systems (MCS) are real-time systems characterized by two or more distinct levels of criticality. In MCS, it is imperative that high-critical flows meet their deadlines while low-critical flows can tolerate some delays. Sharing resources between flows in Network-On-Chip (NoC) can lead to different unpredictable latencies and subsequently complicate the implementation of MCS in many-core architectures. This paper proposes a new virtual channel router designed for MCS deployed over NoCs. The first objective of this router is to reduce the worst-case communication latency of high-critical flows. The second aim is to improve the network use rate and reduce the communication latency for low-critical flows. The proposed router, called DAS (Double Arbiter and Switching router), jointly uses Wormhole and Store And Forward techniques for low and high-critical flows respectively. Simulations with a cycle-accurate SystemC NoC simulator show that, with a 15% network use rate, the communication delay of high-critical flows is reduced by 80% while communication delay of low-critical flow is increased by 18% compared to usual solutions based on routers with multiple virtual channels.