This study introduces a pioneering monitoring system designed to mitigate operational costs and enhance the sustainability of Floating Offshore Wind Turbines (FOWT). The proposed framework combines Autoregressive models with a Stacked Auto-Associativebased Deep Neural Network (AANN-DNN) to detect and classify damages in mooring systems of FOWTs. By extracting damage-sensitive features (DSFs) using the AR models from time-series data and employing unsupervised learning in the auto-associative neural network, followed by supervised training with DNN, the approach demonstrates exceptional accuracy in damage identification and classification. Numerical simulations conducted using NREL's OpenFAST software under diverse metocean conditions validate the method's efficacy, offering a promising solution for efficient FOWT mooring line monitoring.