Carbon Fibre Reinforced Polymer (CFRP) is used in top industries like aerospace, automotive or medicine. Abrasive water jet (AWJ) technology has demonstrated its capacity in machining CFRP parts with a high dimensional accuracy due to its low mechanical loading, reduced machining temperature, high productivity, reduced tooling, and environmental friendliness. An important challenge when machining composite materials with AWJ is material delamination, determined by the high-speed water jet hitting the material during the piercing process. It is the ideal tool for cutting complex CFRP parts, in cases where the piercing point is outside of the workpiece. The challenge lies in machining features where material piercing is required, like holes, slots or internal contours. This paper presents a method of piercing the composite materials with abrasive water jet, that can avoid delamination. The method requires adding the abrasive particles in the water jet at the very beginning of jet formation, thus obtaining a mixed abrasive water jet during the first impact with the composite workpiece. A new cutting system was designed and set up based on the proposed piercing method and was compared with a conventional AWJ cutting system. The insertion of the abrasive particles into the water jet was monitored by using acoustic emission (AE). An analysis of the influence of piercing parameters (water pressure, standoff distance, abrasive inlet angle and abrasive delay time) on the delamination was conducted. The process outcomes such as hole surface integrity, delamination, particles embedment, uncut fibers and dimensional characteristics, were evaluated. The results show that the method is promising in reducing delamination.