A pilot-plant process has been developed based on an innovative laboratory-scale method for the recovery of scandium that exists in economically interesting concentrations in red mud, the main byproduct of alumina production. This method includes acid leaching of the red mud pulp, ion-exchange separation of scandium and lanthanides from the co-leached main elements such as iron, and subsequent liquid-liquid extraction of the eluate for further scandium purification and enrichment. In this work, experimental and theoretical investigation of the pilot-scale leaching process was performed. The following parameters were tested: mode of agitation, solid-to-liquid ratio, acidity of the leachate, number of stages in the process, and pretreatment of red mud with concentrated acids in order to achieve optimum scandium recovery combined with low iron dissolution. Furthermore, by theoretical interpretation of the experimental data, a predictive correlation for the scandium leaching efficiency was developed.