This study introduces a simplified methodology for evaluating the risk of destabilization or damage to floating offshore wind turbines (FOWTs) due to earthquake-induced ground motions, with a focus on FOWTs supported by Tension Leg Platforms (TLP) in seismic regions. The study first reviews the typical hazards experienced by FOWTs supported by Tension Leg Platforms in seismic regions. The proposed analysis workflow is then presented with the methodology exemplified using the prototype TLPWIND turbine as a case study. Detailed analyses are carried out using both horizontal and vertical ground motions. The response of the floating deck and hub levels of the wind turbine to earthquake motions is investigated, and the findings demonstrate that FOWTs are prone to vertical earthquake motions, while horizontal motions have a minor impact. The results show that tension in the cables increases significantly in response to vertical motions, and RNA acceleration outputs for vertical input motions indicate that a considerable acceleration amplification is expectable for large-scale vertical motions, which can cause gear or electrical failures in FOWTs. The proposed methodology provides a useful tool to inform the design and deployment of FOWTs in seismic regions, particularly by accounting for the effects of vertical motions on cable tension and acceleration amplification. The results of this study can enhance the understanding of seismic risks associated with FOWTs and improve current practices in the design and deployment of offshore wind turbines.