As floating offshore wind turbines (FOWTs) gain prominence in deep-water energy exploitation, ensuring the safety of their integrated wet-towing operations under combined wind, wave, and current loads has become paramount. However, a comprehensive understanding of FOWT dynamic behaviors and the associated flow-field evolution under such coupled conditions remains scarce. To bridge this gap, this study presents a high-fidelity, integrated numerical framework for FOWT towing based on computational fluid dynamics (CFD) via STAR-CCM+. Following rigorous grid and time-step convergence verification, the established model was meticulously validated across multiple physical metrics, including airfoil aerodynamic loads, wind turbine performance, and platform free-decay responses. Systematic parametric investigations and comparative coupled simulations reveal distinct operational signatures regarding the three-degree-of-freedom (3-DOF) platform motions. Specifically, current velocity predominantly dictates the mean surge offset and exacerbates low-frequency drift behaviors; regular wave properties govern the response amplitude and dominant frequency of periodic oscillations; and wind exposure prominently scales up the aerodynamic thrust, thereby amplifying the platform pitch response. Furthermore, under wind-wave coupling, irregular waves exhibit distinct broadband frequency characteristics and lower overall response amplitudes compared to their regular counterparts, whilst triggering highly unsteady, fragmented wake structures and complex free-surface deformations. Ultimately, this research offers crucial theoretical foundations, valuable insights into fluid-structure interactions, and practical, actionable guidelines for the stability assessment and logistical transportation optimization of FOWT towing operations.