In this study, a wind turbine spar-buoy floating platform is modeled in the Control-oriented, Reconfigurable, and Acausal Floating Turbine Simulator (CRAFTS), a comprehensive wind turbine simulation tool being developed by the authors, to investigate mooring actuation for stabilizing the surge and pitch motions. The model is validated against the industrial-standard simulator OpenFAST. A reduced-order model of the platform is developed using a mass-spring-damper system (M-K-C system), and the system parameters are estimated. Optimal LQR control gains are obtained for the reduced-order model, and the required actuation forces are calculated using these gains. A control allocation matrix is used to represent the relation between the necessary cable tensions and the required actuation forces from the control system. The performance of the mooring actuation is tested under various load cases: initial perturbations and different sea state conditions with irregular waves. Simulation results demonstrate that surge motion is significantly reduced with moderate changes in cable lengths in both load cases while controlling pitch motion requires higher changes in cable length and is challenging to control under irregular wave conditions.