Engineering optimisation plays a crucial role in addressing a wide range of engineering problems. Parametric optimization is a systematic and efficient approach to determining and adjusting the machining parameters to achieve the best possible machining results. Aluminium and its composites are extensively employed in several automotive industries due to its exceptional properties and high tensile strength. This study examined the aluminium alloy’s capacity to be machined (Al 6061) through the utilization of the abrasive water jet cutting technique. The primary parameters affecting machinability, such as abrasive flow rate, nozzle speed, and stand-off distance, are adjusted to achieve optimal values for output parameters such as material removal rate and depth of penetration. The classical Taguchi approach is not suitable for performing multi-objective optimization. Introducing a novel approach to multi-parameter optimisation, the Grey-Taguchi method is employed in conjunction with the Taguchi method in the Grey Relation Analysis. According to the results, the abrasive flow rate and nozzle speed are the key parameters for achieving improved output values.