The present study focuses on development of prediction models with respect to various cut quality characteristics such as material removal rate, kerf taper and surface roughness for a well-known non-traditional machining process namely abrasive aqua jet cutting (AAJC) of natural fibre composite laminates through combined taguchi-genetic algorithm (TGA) and adaptive neuro fuzzy inference system (ANFIS). The AAJC experiments are conducted based on box-behnken design methodology by considering jet pressure, stand-off distance, traverse speed and wt% of nano clay inclusion in composites as input parameters. The ANFIS parameters are optimized using a hybrid taguchi-genetic training algorithm. The statistical results of hybrid TGA-ANFIS models shows that they are outperformed in prediction of AAJC parameters when compared with the results of multiple-linear regression models. Further, the optimization of AAJC parameters is carried out using a trained ANFIS network and the F-race tuned harmony search algorithm (HSA). The superlative responses such as MRR of 76.9 g/min, KT of 2.23° and Ra of 3.17 µm are forecasted at the optimum cutting conditions such as jet pressure of 303.08 MPa, stand-off distance of 2.16 mm, traverse speed of 375.64 mm/min, and nano clay wt% of 1.27, respectively. The experimental results show that the error between predicted and actual results are lower than 6%, indicating the feasibility of adopting the proposed F-race parametric tuned HSA in optimization of AAJC process.