Recently, the urgency of improved machining performance and environmental sustainability has forced the manufacturer to seek for alternative cooling and lubricating agent/technique such as nano-fluid (NF)-assisted minimum quantity lubrication (MQL). In this context, the performances of aluminum oxide (Al2O3), molybdenum disulfide (MoS2) and graphite (C) NF-impinged MQL in turning of Ti alloy (grade II) using CBN tool were evaluated regarding the cutting force, cutting temperature and surface roughness. The cutting speed, feed rate, approaching angle and cutting conditions (i.e., NFs) were oriented following the Box–Behnken design-of-experiment. The experimental results showed that the graphite NF, compared to Al2O3 and MoS2, revealed the lowest cutting force, temperature and roughness. Moreover, it is evident from SEM images that graphite NF revealed a smoother machined surface and tool profile. This smooth tool and workpiece surface profile can be accredited to graphite’s role as a nano-lubricant and its breaking ability into smaller NFs under pressure. To make the study complete, the adaptive neuro-fuzzy inference system (ANFIS) was employed to predict, the response surface methodology (RSM) was used to mathematically model, and the composite desirability approach (CDA) was used to optimize the responses. A good agreement between the experimental and modeled observations was found; however, the ANFIS outperformed the RSM. Moreover, the analysis of variance exhibited that the cutting force and temperature were primarily influenced by the cutting speed and the surface roughness was afflicted mostly by the feed.