Verifying complex Cyber-Physical Systems (CPS) is increasingly important given the push to deploy safety-critical autonomous features. Unfortunately, traditional verification methods do not scale to the complexity of these systems and do not provide systematic methods to protect verified properties when not all the components can be verified. To address these challenges, this article proposes a real-time mixed-trust computing framework that combines verification and protection. The framework introduces a new task model, where an application task can have both an untrusted and a trusted part. The untrusted part allows complex computations supported by a full OS with a real-time scheduler running in a VM hosted by a trusted hypervisor. The trusted part is executed by another scheduler within the hypervisor and is thus protected from the untrusted part. If the untrusted part fails to finish by a specific time, the trusted part is activated to preserve safety (e.g., prevent a crash) including its timing guarantees. This framework is the first allowing the use of untrusted components for CPS critical functions while preserving logical and timing guarantees, even in the presence of malicious attackers. We present the framework its schedulability analysis and the coordination protocol between the trusted and untrusted parts. Our implementation on a Raspberry Pi 3 is also discussed along with experiments showing the behavior of the system under failures of untrusted components, and a drone application to demonstrate its practicality.