Offshore wind energy is increasingly being realized at deeper ocean depths where jacket foundations are now the greatest choice for dealing with the hostile environment. The structural stability of these undersea constructions is critical. This paper states a methodology to detect and classify damage in a jacket-type support structure for offshore wind turbines. Because of the existence of unknown external disturbances (wind and waves), standard structural health monitoring technologies, such as guided waves, cannot be used directly in this application. Therefore, using vibration-response-only accelerometer measurements, a methodology based on two in-cascade Siamese convolutional neural networks is proposed. The first Siamese network detects the damage (discerns whether the structure is healthy or damaged). Then, in case damage is detected, a second Siamese network determines the damage diagnosis (classifies the type of damage). The main results and claims of the proposed methodology are the following ones: (i) It is solely dependent on accelerometer sensor output vibration data, (ii) it detects damage and classifies the type of damage, (iii) it operates in all wind turbine regions of operation, (iv) it requires less data to train since it is built on Siamese convolutional neural networks, which can learn from very little data compared to standard machine/deep learning algorithms, (v) it is validated in a scaled-down experimental laboratory setup, and (vi) its feasibility is demonstrated as all computed metrics (accuracy, precision, recall, and F1 score) for the obtained results remain above 96%.