Stability is the most important criterion for the safe operation of floating offshore wind turbines (FOWTs). Mooring lines are generally used for FOWTs to keep them in a particular position and failure of mooring lines may induce the damage to the FOWTs. Therefore, it is necessary to study the dynamic response of FOWT following mooring failure. The dynamic response of FOWT will increase rapidly due to mooring failure. Hence, tuned mass damper (TMD) is used in this paper for mitigating the response of FOWT. The TMD is installed in the nacelle part of the wind turbine and the model uncertainties are also considered during the design of TMD. The ITI Energy barge-type floating platform is considered in the present paper for supporting NREL 5 MW wind turbine. The failure of the single mooring line for ITI Energy barge FOWT with TMD is numerically simulated using the open-source code OpenFAST. The environmental conditions corresponding to the above cut-in and around cut-out wind speed are considered for simulating the operating condition of FOWT. It is found that the platform responses are very large due to mooring failure. The maximum surge, sway, roll, and yaw responses are increased by 169%, 643%, 190%, and 336%, respectively, for mooring failure compared to intact mooring in the above cut-in wind speed condition. It is also noted that the TMD is more useful for mitigating the dynamic response of FOWT following mooring failure. The maximum values of roll and pitch platform responses are decreased by 21% and 5.5%, respectively, for mooring failure with TMD than for without TMD case in the above cut-in wind speed condition.