The application of structural control to offshore wind turbines (OWTs) using tuned mass dampers (TMDs) has shown to be effective in reducing the system loads. The parameters of a magnetorheological (MR) damper modeled by the Bouc‐Wen model are modified to utilize it as a damping device of the TMD. Rather than showcasing the intricate design policy, this research focuses on the availability of the MR damper model on TMDs and its significance on structural control. The impact of passive and semiactive (S‐A) TMDs applied to both fixed bottom and floating OWTs is evaluated under the fatigue limit state (FLS) and the ultimate limit state (ULS). Different S‐A control logics based on the ground hook (GH) control policy are implemented, and the frequency response of each algorithm is investigated. It is shown that the performance of each algorithm varies according to the load conditions such as a normal operation and an extreme case. Fully coupled time domain simulations are conducted through a newly developed simulation tool, integrated into FASTv8. Compared with the passive TMD, it is shown that the S‐A TMD results in higher load reductions with smaller strokes under both the FLS and the ULS conditions. The S‐A TMD using displacement‐based GH control is capable of reducing the fore‐aft and side‐to‐side damage equivalent loads for the monopile by approximately 12% and 64%, respectively. The ultimate loadings at the tower base for the floating substructure are reduced by 9% with the S‐A TMD followed by inverse velocity‐based GH control (IVB‐GH).