Floating offshore wind (FOW) is one of the top emerging forms of renewable power. However, the current share of floating wind is minimal when compared to fixed offshore wind and onshore wind. The main reason for this is the fact that its operation and maintenance costs are too high. New technologies, such as deep learning algorithms, can help reduce these costs by optimizing maintenance strategies. In this study, we propose a method for the structural health monitoring (SHM) of mooring systems for floating offshore wind turbines. In particular, we detect failure by implementing an autoencoder, whose inputs are statistics extracted from the floater’s response to a set of environmental conditions. This approach allows for the early identification of mooring failure, which is key for SHM purposes, as late maintenance leads to performance loss and increased downtime. To maximize the network’s accuracy, we test the performance of numerous architecture designs using automated machine learning techniques. FOW research stands at a much earlier stage than onshore wind, and hence samples of real data are scarce. We therefore base our analysis on data obtained from OpenFAST simulations. Damage is induced in such a way that the data set contains more samples of undamaged and mildly damaged mooring lines. This, once the algorithm is trained, should allow for the identification of damage at a much earlier stage. We employ high-performance computing (HPC) clusters to generate over 100,000 samples, which we then use to first train the network’s decoder. Once trained, we save its weights and biases in order to test multiple encoder architectures without having to retrain the network, thus keeping training computationally efficient. The proposed algorithm is capable of detecting even very small defects caused by biofouling and anchor displacements, with correlation coefficients reaching values over 93.2% and 99.1%, respectively. To simplify the interpretation of the results, we categorized each form of damage. Using this approach, we observe a minimum severity threshold at which the platform’s behavior changes significantly and therefore maintenance operations should be performed. The obtained results show promise when dealing with undamaged or severely damaged mooring lines. We analyze the errors between true and predicted categories to discover that mismatches occur mostly when the true damage coefficients are close to the boundaries between consecutive classes.