This study uses the acoustic emission structural health monitoring method to identify fracture mechanisms in composite bonded joints when varying the substrate stacking sequence. Quasi-static mode I loading tests were performed on secondary adhesively bonded multidirectional composite substrates (0, 90, 45, −45, 60 and −60° fibre orientations). An unsupervised artificial neural network combined with the visual fracture evaluation of the specimens and the Morlet continuous wavelet transform was used to cluster and give the acoustic emission signals a physical meaning. Different fracture mechanisms could be identified within the adhesive layer (i.e., cohesive failure) and in the composite substrates, including non-visible damage mechanisms (matrix micro-cracking, fibre/matrix debonding, fibre pull-out and fibre breakage). Using the Morlet continuous wavelet transform, it was possible to recognise that the highest peak frequency does not always represent the most relevant signature of the fracture mechanism. Moreover, multiple peak frequencies can be associated with multiple fracture mechanisms, such as the fibre pull-out that occurs in the combination of matrix cracking and fibre breakage. Furthermore, no differences were observed in mode I loading conditions between the acoustic emission signatures from the cohesive failure in the adhesive layer and the matrix cracking within the composite substrate. The findings of this study present a great opportunity to gain more insight into the fracture behaviour of polymer materials and fibre-reinforced polymer materials and to improve the quality of adhesively bonded joints.