The Technical University of Denmark (DTU) 10 MW wind turbine is selected as the object of this study. The braceless semi-submersible platform for the National Renewable Energy Laboratory 5 MW wind turbine is upscaled to support the DTU 10 MW wind turbine. The servo control system of the 10 MW semi-submersible wind turbine is redesigned. Furthermore, torque control is performed below the rated wind speed to achieve maximum power capture, and the gain scheduling proportional integral (GSPI) control method is performed above the rated wind speed to realize the design of the variable propeller control system. This ensures the safe operation of the floating wind turbine above the rated wind speed. The reliability of the designed servo control system is verified by a full coupling dynamic response analysis with the designed servo control system, aerodynamics, and hydrodynamics under the combined action of wind and waves. The coupled dynamic characteristics of the 10 MW semi-submersible wind turbine under different conditions are analyzed, including operational, extreme, and fault situations. The results show that the servo control system effectively controls the motion response of a 10 MW floating offshore wind turbine (FOWT). Turbulent wind has an obvious excitation effect on the surge and pitch of the FOWT, whereas the heave motion is primarily excited by wave loads. Different fault conditions can cause different motion and structural responses. Furthermore, the tower top bending moment is greatly affected by the imbalance of aerodynamic load, and the surge, pitch motion, tower base bending moment, and mooring tension of the FOWT are affected by different fault conditions to varying degrees. In addition, the heave motion is generally barely affected by the fault conditions.