The damage initiation and evolution of carbon fiber-reinforced polymer (CFRP) composite under multi-axial loading is of fundamental interest. This study investigates intra- and interlaminar damage modes induced in open-hole quasi-isotropic (QI) carbon/epoxy composite laminate under combined tension-shear loading using the acoustic emission (AE) technique. The effect of layer thickness is studied using three types of laminates with stacking sequences PL-1: [−452/452/902/02]s, PL-2: [−453/453/903/03]s (ply blocked), and SL-1: [−45/45/90/0]2s (a sub-laminate blocked or distributed). Clustering of acquired AE signals is carried out using hierarchical methods. Damage modes evolution for the open hole QI CFRP is captured using the clustered AE signal data. It is observed that the thickness scaling significantly affects the open-hole strength and the critical failure mechanisms. Dominant damage mechanisms are identified based on AE cumulative energy. Ply-level blocked (PL-1 and PL-2) laminates exhibit lower strength than the SL-1 blocked laminate. The findings from this experimental investigation indicate that the AE technique in conjunction with the clustering approach is a prospective tool for the structural health monitoring of composite structures under combined loading.