This paper aims at investigating the effects of variable traverse speeds on machining-induced damage of fibre-reinforced composites, using the abrasive water jet (AWJ) drilling. Three different types of epoxy-based composites laminates fabricated by vacuum bagging technique containing unidirectional (UD) flax, hybrid carbon-flax and carbon fibre-reinforced composite were used. The drilling parameters used were traverse speeds of 20, 40, 60 and 80 mm/min, constant water jet pressure of 300 MPa and a hole diameter of 10 mm. The results obtained depict that the traverse speed had a significant effect with respect to both surface roughness and delamination drilling-induced damage responses. Evidently, an increase in water jet traverse speed caused an increase in both damage responses of the three samples. Significantly, the CFRP composite sample recorded the lowest surface roughness damage response, followed by C-FFRP, while FFRP exhibited the highest. However, samples of FFRP and hybrid C-FFRP recorded lowest and highest delamination damage responses, respectively. The discrepancy in both damage responses, as further validated with micrographs of colour video microscopy (CVM), scanning electron microscopy (SEM) and X-ray micro-computed tomography (X-ray μCT), is attributed to the different mechanical properties of the reinforced fibres, fibre orientation/ply stacking and hybridisation of the samples.