This paper presents the analysis of average surface roughness, cutting force, and feed force in turning of difficult-to-machine Ti-6Al-4V alloy by experimental investigation and performance modeling. Based on knowledge of the literature, to pacify the elevated temperature in machining Ti-6Al-4V and to ensure a clean environment, the experiments are carried out in cryogenic (liquid nitrogen) condition by following the Taguchi L18 mixed-level orthogonal array. Afterward, the models of responses have been formulated by the response surface methodology (RSM) and artificial neural network (ANN). The higher values of correlation coefficient (≥96%) and lower values of error determined the adequacy of the developed models. Comparative study of both models revealed that the RSM-based model revealed greater accuracy for the testing data and hence recommended. Analysis of variance (ANOVA) determined the effects of cutting speed, feed rate, and insert configuration on the quality characteristics. The results revealed that a cutting speed not exceeding 110 m/min is likely to generate favorable machining responses. In addition, the higher feed rate was found to ensure better machining performances. Moreover, the desirability-based multi-response optimization determined that a cutting speed of 78 m/min, a feed rate of 0.16 mm/rev, and use of the SNMM tool insert are capable of minimizing surface roughness at 1.05 μm, main cutting force at 315 N, and feed force at 208 N.