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When floating offshore wind turbines (FOWT) encounter extreme waves in operation, it is a highly nonlinear system involving floater motion and extreme wave–structure interactions. The behavior is crucial for floating offshore wind turbine safety. With the aid of a high-fidelity CFD solver, a harmonic separation method through a ‘Stokes-like’ formulation was adopted to obtain the parameters for each harmonic response. The present study focuses on analyzing higher harmonic load, dynamic motion response, and tension load of the mooring line the DeepCwind semi-submersible FOWT. The results show that the higher-harmonic wave load cannot be ignored in the extreme marine environment, the second harmonic can be over 16% of the linear wave load, and the third harmonic can be over 10% of the linear wave load with large wave steepness. The duration of a focused wave crest interaction with the platform is a short process of only 1.4 s in model scale, corresponding to about 10 s for the prototype. The wave runup at the upstream column is larger than the other columns, and the flow velocity is double that of the wave without the floater in presence. The dynamic response of the floater contains two phases, ’forced oscillations’ is identified to be drag-driven from odd harmonics , and ’free decay’ mainly comes from second-order difference-frequency influence from even harmonics. The properly normalized wave forces of surge and heave motion are not influenced by steepness k p A l i n e a r . For surge motion , the total motion mainly comes from the nonlinear low frequency component. For pitch motion, the linear response is dominant in small k p A l i n e a r . When the steepness k p A l i n e a r increases gradually, the second-order low-frequency response of pitch motion will increase rapidly and dominate the total response. • A series of numerical investigations of focused wave groups interaction with semi-submersible floating offshore wind turbine are performed. • The higher-harmonic wave loads and low frequency resonance response are obtained by phase-decomposition method. • The dynamic response of the floater contains two phases: ‘forced oscillations’ as drag-driven from odd harmonics and ‘free decay’ from 2nd-order diff-frequency influence from even harmonics. • Higher-harmonic wave load cannot be ignored in the extreme marine environment, the 2nd harmonic can be over 16% of the linear wave load in large wave steepness.