Dynamic simulators of semi-autogenous grinding (SAG) mills are essential tools for process optimization, operational analysis, and predictive maintenance in mineral processing plants. However, the limited availability of reliable industrial measurements often constrains the development and validation of fully dynamic models. This work presents the development of a physics-based dynamic SAG mill simulator designed to reproduce physically consistent steady-state and transient behavior under realistic operating conditions. The simulator relies on the generation of synthetic yet physically representative particle size distributions using Rosin–Rammler laws and on rigorous internal mass balance formulations. The governing equations follow a non-stationary population balance approach describing internal breakage, classification, mill filling, grinding media effects, water content, and power consumption. Effective breakage rates are analytically derived from steady-state mass balances, ensuring strict mass conservation and internal consistency across all size classes. Mill dynamics are described through a time-dependent formulation of internal charge evolution and filling level, enabling the simulation of transient responses to operational disturbances. Power draw is computed using a phenomenological correlation, while charge geometry indicators, including toe and shoulder angles, are evaluated as functions of mill filling and operating state. The simulator is tested under representative industrial-scale conditions with a nominal feed rate of 1700 t/h and subjected to controlled disturbances, including a 10% increase in feed rate and a 20% increase in critical speed fraction. The resulting responses of mill filling, power consumption, and charge geometry exhibit realistic trends and causal relationships consistent with behaviors reported in the literature for industrial SAG mills. The developed simulator provides a practical computational tool for mining operators to analyze operating strategies, explore what-if scenarios, and assess the impact of key operating variables on grinding performance and energy consumption, forming a physically consistent core for optimization studies and future digital twin developments.