The concept of installing two wind turbines on a floating platform, known as a floating twin-rotor wind turbine system, has recently garnered significant interest. This configuration can harness greater wind energy resources, reduce installation and mooring costs by sharing mooring lines, and minimize losses due to wake effects between turbines through yaw control. However, previous research has not sufficiently addressed the dynamic performance analysis of such systems. This study focuses on a high-capacity floating twin-rotor wind turbine system and develops an aero-hydrodynamic coupled analysis method based on the free vortex wake method and potential flow theory, specifically tailored for the twin-rotor configuration. This method facilitates real-time iterative calculations of wind and wave loads acting on the system and suggests optimization strategies for its design. Our findings indicate that the design of high-capacity floating twin-rotor systems can significantly reduce costs. Furthermore, the twin-rotor floating system design enhances wake recovery and achieves optimal comprehensive performance when the rotor spacing ratio (S/D) is 1.2 for the IEA 15 MW turbine. The coupled interactions induce periodic variations in aerodynamic performance, with the amplitude of these variations increasing with turbulence intensity. This research lays a theoretical foundation for advancing the design, platform optimization, and coupled computational analyses of large-capacity, large-scale floating twin-rotor wind turbine systems.