Carbon fiber-reinforced polymer (CFRP) composites are of high interest in the field of aerospace because of their extremely high strength-to-weight and stiffness-to-weight ratios. Dry processing has been widely applied due to the hygrothermal aging of CFRP using flood lubrication. However, severe conditions of dry machining lead to an abundance of multifarious defects and dust harmful to humans and the environment. The increasing vegetable oil-based nanofluid minimum quantity lubrication (NMQL) involving CNTs with excellent heat transfer and friction reduction could solve the above technique bottleneck. Grinding experiments under different conditions were conducted to investigate the CFRP grindability of NMQL. Results show that compared with dry grinding, the surface roughness Ra, Rz, and RSm values of CNT NMQL in the feed direction (fiber direction) are reduced by 17.70%, 20.78%, and 25.40% (12.68%, 25.06%, and 11.43%), respectively. Furthermore, the 3D fractal dimension of NMQL grinding was the lowest, and the spectral width and difference were decreased by 21.76% and 31%, respectively. The texture features of the machined surface roughness of NMQL demonstrated the least changes, in which the energy proportion of the high-frequency detail signal was reduced by 46.85% compared with dry grinding. The energy proportion of detail sub-images in the NMQL grinding SEM wavelet decomposition diagram was the lowest (0.4214). The proportion of the defect characteristics in the horizontal direction (0.155) was less than the vertical direction (0.1952). This finding was consistent with the energy proportion of the surface roughness signal wavelet analysis. This study demonstrated the feasibility of CFRP precision machining using NMQL.