This paper describes the important significance of cutting-edge technology in the machining of polycrystalline diamond (PCD) cutting inserts by comparing the evaluation criteria. The LASER technology of cutting-edge machining is compared with grinding and electrical discharge machining (EDM) technologies. To evaluate the data from the experiments, the Grey Relational Analysis (GRA) method was used to optimize the input factors of turning to achieve the required output parameters, namely the deviation of roundness and chip cross-section. The input factors of cutting speed, feed rate, depth of cut and corner radius were applied in the experiment for three different levels (minimum, medium and maximum). The optimal input factors for turning of aluminum alloy (AW 5083) were determined for the factorial plan according to Grey Relational Grade based on the GRA method for the multi-criteria of the output parameters. The results were confirmed by a verification test according to the GRA method and optimal values of input factors were recommended for the machining of Al-alloy (AW 5083) products. This material is currently being developed by engineers for forming selected components for the automotive and railway industries, mainly to reduce weight and energy costs. The best values of the output parameters were obtained at a cutting speed of 870 m/min, feed rate of 0.1 mm/min, depth of cut of 0.5 mm and a corner radius of 1.2 mm.