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The sonocatalytic activity of nano-sized ZnO powder was studied via the degradation of the Direct Blue 71 azo dye. The nano-sized ZnO powder that was selected was the same as that which was synthesized and characterized in our previous study. The influences of six operational parameters including the initial pH, the initial concentration, the dose of sonocatalyst, the ultrasound frequency, the ultrasound power, and the process time were investigated on the basis of process efficiency and energy consumption. The design of experiments was applied and the experiments were conducted according to the design. The experiments were carried out in a batch reactor. The experimentally obtained dye removal percent (DR%) and the energy consumption per mass ranged from 0.03–100 and 0.19–1273 (wh/g), respectively. The data were used for modelling by using reduced quadratic multiple regression models and the artificial neural network (ANN). Multi-objective optimization of DR% and EPM was applied by using the genetic algorithm (GA) over the outperformed ANN models. The mineralization was studied using total organic carbon analysis. The study indicated promising results in the application of both the novel sonocatalyst and the Artificial Intelligent Approaches.