Concrete, ceramics, rocks, metal-matrix composites, titanium alloys and other hard-to-cut materials are frequently cut using the non-traditional cold processing method known as abrasive water jet machining (AWJM). A virtual machining system is proposed in the study to minimize roughness of surface and residual stress during AWJM of titanium alloy Ti6Al4V. The water and workpiece are simulated in virtual environments using the smoothed particle hydrodynamics (SPH) approach and finite element method, respectively. Then, the Johnson–Cook law model of titanium alloy is used to obtain the cutting temperature during cutting operations. To calculate residual stress during the AWJM operations, the finite element method is then utilized. The Taguchi optimization method is implemented to minimize surface roughness and residual stress in AWJM operations. Thus, the optimized machining parameters such as water jet pressure, traverse speed, abrasive mass flow rate and standoff distance are calculated to minimize the surface roughness and residual stress during the AWJM of titanium alloy Ti6Al4V. Experimental and computational examinations are carried out in order to validate the effectiveness and efficiency of proposed virtual machining system in minimization of surface roughness and residual stress during abrasive waterjet cutting of titanium alloy Ti6Al4V. As a result, by using the optimized machining parameters, 23.7% and 27.1% reduction in the measured and predicted residual stress of sample machined part are obtained. Also, the sample machined part's surface roughness is reduced by 26.7% and 27.9%, for the measured and predicted surface roughness of sample machined part, respectively. So, the quality and reliability of the machined parts can be enhanced using the developed virtual machining system in the study to minimize the surface roughness and residual stress in AWJM operations. [ABSTRACT FROM AUTHOR]