This research aims to provide a novel nanofluid / minimal lubrication (MQL) technology for 7075-T6 aluminum alloy microdeep drilling. This technology will extend the life of tools used for precision machining. A parameter combination meeting the optimal quality-related objectives was obtained, and a predictive model was developed. Because microdrilling force and torque were two quality-related objectives, this study adopted Taguchi’s robust design, used machining parameters (i.e., nanofluid weight percentage concentration, spindle speed, feed rate, nozzle distance, nozzle angle, MQL flow, air compression, and pecking depth), and performed grey relational analyses to obtain the parameter combination generating the optimal microdrilling force and torque. Subsequently, this study used a neural network and conducted Taguchi grey relational analyses (where Taguchi orthogonal tables were used as the experimental basis and the experimental data from grey relational analyses were used as training examples) to develop a highly accurate microdrilling predictive model. The parameter combination for generating the optimal microdrilling force and torque predicted differed from those of the experiment results by only 0.44% and 1.24%.