In the current precision industry, the rapid production of high-quality parts in bulk quantities has led to high competitiveness. In this study, the Taguchi method and grey relational analysis (GRA) approach were used in a practical investigation of precision lathe processing. The purpose was to find optimal parameters for single-target and multitarget cutting. The production of targets of the highest quality was the research focus, with the aim of strengthening the links between this study and the application to the processing industry. Precision, surface roughness, and material removal rate were selected as targets for improvement. The parameters commonly used for lathe processing were set as control factors, and cutting depth, spindle speed, feed rate, and material elongation were set as experimental factors. The results showed that in the cutting of materials, cutting precision was mainly affected by the depth of cut and spindle speed, surface roughness by spindle speed, and the material removal rate by the cutting depth. In a comparison of the quality loss for the same materials using previous parameters, the cutting precision has about 64 to 99% optimization, the surface roughness has 69 to 96% optimization, and the material removal rate has more than 90% optimization. GRA was also employed to analyze the sequences of parameters from the Taguchi experiments to obtain the target relationships and to find the various combinations of factors for improvement.