The demand for the machining and cutting of plastic parts is in continuous increase. The present study is intended to investigate the optimization of high density polyethylene (HDPE100) orthogonal turning operation using the Grey Relational Analysis (GRA). Accordingly, experimental tests based on Taguchi method are performed to establish a correlation between cutting parameters on one hand and machining force, specific cutting force and roughness of machined surface on the other hand. An optimal parameters combination for the turning process is obtained. In addition to regression models deduction, the analysis of variance (ANOVA) is applied to identify the most significant factors. It is found that the order of the importance of controllable factors to the tangential cutting force (Ft) is feed rate (f), depth of cut (ap) and cutting speed (Vc). However, when considering the importance with respect to specific cutting force (Ks), the order becomes (Vc), (ap) and (f). Finally, the order of cutting parameters according to mean roughness criteria, represented by (Ra), (Rz) and (Rt), shifts to (f), (Vc) and (ap). The optimized cutting regime ensuring minimization of roughness and cutting forces is well described by Vc = 188 m/min, f = 0.14 mm/rev and ap = 3 mm. This study unveiled new approaches based on combined GRA and ANOVA for machining other polymers such as tough reinforced polymers and composites used as human prosthesis.