In case of hard-to-cut materials, as titanium alloy Ti6Al4V, eco-friendly cooling methods or their modifications are still being developed. Therefore, various types of nanofluids are applied in the cutting process to reduce friction in the cutting zone and thus heat accumulation in the tool corner. This paper presents an analysis of the selected tool wear indicators, as well as the wear mechanisms, after turning with various cooling/lubricating techniques, including: MQL with the addition of copper nanoparticles (CuNPs), dry machining and the MQL technique without nanoparticles. Four sizes of CuNPs were applied: 22 nm, 35 nm, 65 nm and 80 nm. Analysis of SEM images and maps of elemental distributions on the cutting edge working surfaces allowed to determine that the smallest sizes of copper nanoparticles introduced in the cutting fluid result in reduced tool flank wear, as well as the reduced width and depth of the crater wear on the rake face. With the smallest size of copper nanoparticles, a “ball bearing” and tribofilm formation effects were obtained, which prevented intense adhesive and abrasive wear. Turning, applying MQL + CuNPS 22 nm method resulted in a decrease of selected tool wear rates from 25.7% to 55% compared to effects reached during dry machining, and from 11.7% to 39.2% compared to effects of MQL turning without addition of nanoparticles to the cutting fluid.