The purpose of this study is to optimize different operational parameters, such as the nozzle diameter, traverse velocity, standoff distance, and pump pressure, with reference to cutting efficiency parameters, namely, depth and width of cut, in the cutting operation using a pure water jet on Sardinian basalt samples. Width of cut, which has not been previously mentioned in literature, was used as the second cutting efficiency parameter in this study. Also, 37 water jet cutting tests on Sardinian basalt samples were carried out based on the factorial design of the experiment at two levels and with the four operational parameters given above using Design Expert 7.0. In addition to these cutting tests, control and repetition tests were also performed and in total, 72 cutting operations were made in this study. The two-factor interaction (2FI) model was developed utilizing experimental measurements for the depth and width of cut after performing 37 cutting operations. The adequacy of the predicted regression model equations was tested using the very well-known method of analysis of variance. These model equations were used to optimize the operational parameters for the desired depth and width of cut. Cuttability charts indicating the optimum working point with respect to the depth and width of cut for Sardinian basalt samples were developed and presented in this study. These charts could be of help in the natural stone industry in terms of a more efficient usage of the water jet cutting machine. As a result of this study, the optimum values of working parameters for Sardinian basalt stone samples were found to be 0.8 mm for the nozzle diameter, 90 MPa for the pressure, 5 mm for the standoff distance, and 4 m/min for the traverse velocity for the pure water jet cutting system. In these optimum cutting conditions, a depth of 7.694 mm and a width of 1.986 mm were predicted to be the cutting values. These values go well with the measurements.