The investigation of the floating offshore wind turbines (FOWT) under accidental conditions is more important owing to post-accident transient motions of the FOWT. The breakage of the mooring line is considered as an accidental event in this paper and the effects of a tuned mass damper (TMD) on the coupled dynamic response reduction is explored. The model uncertainties have also been incorporated in the design of TMD and the TMD is located in nacelle for the simulation. The dynamic behavior of the ITI barge-type floating platform supporting the NREL 5 MW turbine is studied in this paper and the breakage of a single mooring is simulated. The impact of the breakage on the responses of the platform, fairlead tensions, and tower motions are investigated using the open-source code OpenFAST. It is noted that the surge, sway, roll, and yaw platform responses are very large after the breakage. The maximum mooring line fairlead tensions of all the lines are within the breaking strength even after the mooring failure. It is also observed that the TMD is more helpful in bringing down the platform roll, pitch motions, displacement of the tower, and moment of the tower (X-direction).