Industrial wireless sensor networks are becoming popular for critical monitoring and control applications in industrial automation systems. For such type of applications, providing reliable real-time performance regarding data delivery is considered as a fundamental challenge. The problem becomes more prominent with mixed-criticality systems, where different data flow with different levels of criticality (importance) coexist and characterized by different requirements regarding delay and reliability. In this paper, we propose a wireless fieldbus protocol to enable real-time communication and service differentiation for cluster-based mixed-criticality networks. A process monitoring scenario of plastic extrusion is used to define the protocol requirements and elaborate the working principle of the proposed work. In our proposed protocol, each data flow is scheduled for channel access based on its criticality level using a distributed prioritized medium access mechanism that ensures a guaranteed channel access for the most critical traffic over other traffic types. The performance of the proposed protocol is analyzed analytically using a discrete-time Markov chain model to evaluate the performance in terms of delay and throughput. Moreover, the extensive simulations are conducted to prove the analytical claims and different performance assessments are provided, which also demonstrate the effectiveness of the proposed approach compared with the related existing work.