Machining of hard and brittle materials such as engineering ceramics, glass, and silicon is a formidable task. Unlike cutting processes employing plasma and lasers, better machining capabilities of abrasive jet machining are characterized by thermally damaged free surface which is highly competitive as well as important for survival of materials in service. In this paper, an attempt has been made to combine hot abrasives and compressed air to form a hot abrasive air jet. This study aims to analyze the cutting performance in hot-abrasive jet machining (HAJM) of hardstone quartz concerning surface roughness, taper angle (TA), and material removal rate (MRR). Combined approach of Box–Behnken design — analysis of variance, response surface methodology, and statistical technique (here desirability function approach), followed by computational approach (here genetic algorithm), is, respectively, employed for experimental investigation, predictive modeling, and multi-response optimization. Thereafter, the effectiveness of proposed two multi-objective optimization techniques is evaluated by confirmation test and subsequently, the best optimal solution (i.e. at air pressure of 7kgf/cm2, abrasive temperature of 64∘C, stand-off distance of 4 mm) is used for economic analysis. Result shows that the most significant parameter is abrasive temperature for surface roughness, whereas it is pressure in case of both TA and MRR. Applications of hot abrasives in AJM process have shown attention in enhancing the cutting performance for material removal. Due to lower percentage contribution of error (6.68% to Rz, 9.89% to TA, and 6.42% in case of MRR), a higher correlation coefficient (R2) was obtained with the quadratic regression model, which showed values of 0.92, 0.9, and 0.93 for surface roughness, TA, and MRR, respectively.