Connected automated vehicles (CAVs) have shown great potential in improving traffic throughput and stability. Although various longitudinal control strategies have been developed for CAVs to achieve string stability in mixed-autonomy traffic systems, the potential impact of these controllers on safety has not yet been fully addressed. This paper proposes safety-critical traffic control (STC) by CAVs—a strategy that allows a CAV to maintain safety relative to both the preceding vehicle and the following human-driven vehicles (HVs). Specifically, we utilize control barrier functions (CBFs) to impart collision-free behavior with formal safety guarantees to the closed-loop system. The safety of both the CAV and HVs is incorporated into the framework through a quadratic program-based controller that minimizes deviation from a nominal stabilizing traffic controller subject to CBF-based safety constraints. Considering that some state information of the following HVs may be unavailable to the CAV, we employ state observer-based CBFs for STC. Finally, we conduct extensive numerical simulations – that include vehicle trajectories from real data – to demonstrate the efficacy of the proposed approach in achieving provably safe traffic.