Endowed with automation and connectivity, Connected and Automated Vehicles are meant to be a revolutionary promoter for Cooperative Driving Automation. Nevertheless, CAVs need high-fidelity perception information on their surroundings, which is available but costly to collect from various onboard sensors as well as vehicle-to-everything (V2X) communications. Therefore, authentic perception information based on high-fidelity sensors via a cost-effective platform is crucial for enabling CDA-related research, e.g., cooperative decision-making or control. Most state-of-the-art traffic simulation studies for CAVs rely on situation-awareness information by directly calling on intrinsic attributes of the objects, which impedes the reliability and fidelity of the assessment of CDA algorithms. In this study, a \textit{Cyber Mobility Mirror (CMM)} Co-Simulation Platform is designed for enabling CDA by providing authentic perception information. The \textit{CMM} Co-Simulation Platform can emulate the real world with a high-fidelity sensor perception system and a cyber world with a real-time rebuilding system acting as a "\textit{Mirror}" of the real-world environment. Concretely, the real-world simulator is mainly in charge of simulating the traffic environment, sensors, as well as the authentic perception process. The mirror-world simulator is responsible for rebuilding objects and providing their information as intrinsic attributes of the simulator to support the development and evaluation of CDA algorithms. To illustrate the functionality of the proposed co-simulation platform, a roadside LiDAR-based vehicle perception system for enabling CDA is prototyped as a study case. Specific traffic environments and CDA tasks are designed for experiments whose results are demonstrated and analyzed to show the performance of the platform.