The moorings of the Floating Wind Turbine (FWT) platforms, long term suffering from the coupling loads of wind, waves and currents, are especially prone to structural fatigue. The purpose of this study is to mine effective information from the dynamic response of the FWT platform to achieve early damage detection for mooring health conditions. However, high nonlinearity of the FWT platform dynamic response, that is caused by the complexity of the working environment, hinders the accuracy of fatigue analysis and damage detection, Therefore, in this study, motivated by the accuracy of the chaotic features in quantifying nonlinearities and reliability of the convolutional neural network for feature extraction, an intelligent damage detection model, named Convolutional Neural Network-t-distribution Stochastic Neighbor Embedding (CNN-t-SNE), is proposed to automatically detect the damage magnitude of the moorings. Through analyzing the dynamics of FWT platform mooring from structure creep to failure, it is found that the yaw response is the most sensitive to structural damage. To examine the reliability of the proposed CNN-t-SNE method, the Lyapunov exponent and chaotic attractor quantify the nonlinearity of the features in the neural networks to indicate that the nonlinearity of the features decreases as the neural network layer deepens.