Global sensitivity analysis (GSA) is a fundamental tool for identifying input variables that determine the behavior of the mathematical models under uncertainty. Among the methods proposed to perform GSA, those based on the Sobol method are highlighted because of their versatility and robustness; however, applications using complex models are impractical owing to their significant processing time. This research proposes a methodology to accelerate GSA via surrogate models based on the modern design of experiments and supervised machine learning (SML) tools. Three case studies based on an SAG mill and cell bank are presented to illustrate the applicability of the proposed procedure. The first two consider batch training for SML tools included in the Python and R programming languages, and the third considers online sequential (OS) training for an extreme learning machine (ELM). The results reveal significant computational gains from the methodology proposed. In addition, GSA enables the quantification of the impact of critical input variables on metallurgical process performance, such as ore hardness, ore size, and superficial air velocity, which has only been reported in the literature from an experimental standpoint. Finally, GSA-OS-ELM opens the door to estimating online sensitivity indices for the equipment used in mineral processing.