Mine integrated energy system (MIES) can promote the utilization of derived energy and achieve multi-energy complementation and ecological protection. Now it gradually becomes an important focus for scientific carbon reduction and carbon neutrality. To reduce the impact of uncertain prediction differences on the system during the process of using mine derived energy, a low-carbon economic operation strategy of MIES considering energy supply uncertainty is developed in this paper. Firstly, based on the basic structure of energy flow in MIES, the energy-carbon flow framework of MIES is established for the low-carbon operation requirements. Secondly, considering carbon emission constraints, the low-carbon economic operation optimization model (LEOOM) is built for MIES to minimize operation cost and carbon emission. Finally, multiple uncertainties of the system are modeled and analyzed by using the robust model under the risk aversion strategy of information gap decision theory (IGDT), and a model conversion method is designed to optimize the low-carbon economic operation model. The simulation results under three scenarios demonstrate that compared to the existed economic dispatching models, the proposed model achieves a 30% reduction in carbon emission while the operational cost of MIES only is increased by 2.1%. The model efficiently mitigates the carbon emission of the system, and the proposed uncertain treatment strategy can significantly improve the robustness of obtained operation plans.