Geothermal energy extraction through deep mine systems offers the potential to reduce the cost of geothermal systems while meeting the cooling needs of deep mines. However, the injection of cold water into the subsurface triggers strongly coupled thermo-hydro-mechanical (THM) processes that can affect the stability of underground excavations. This study evaluates the impact of geothermal energy extraction on the temperature and stability of a deep mine. By quantifying the sensitivity of the mine temperature and stability to various parameters, we propose a scheme to optimize geothermal energy production, while achieving rapid mine cooling and maintaining stability. We first evaluate the impact of geothermal operations on mine temperature and stability through THM numerical modeling. The simulations show that poro-elastic stress quickly affects mine stability, while thermal stress has a more significant impact on the long-term stability. We then use Distance-based Generalized Sensitivity Analysis (DGSA) to quantify parameter sensitivity. The analysis identifies the distance between the mine system and the geothermal system as the most influential factor. Other important parameters include the injection rate, injection temperature, well spacing, coefficient of thermal expansion, permeability, Young's modulus, and heat capacity. Finally, we propose a DGSA-based optimization framework that accounts for subsurface uncertainty and validate the optimized results. Our results indicate that, with favorable geological conditions, a rational selection of system design parameters can enhance geothermal energy production while ensuring rapid mine cooling and stability. This study provides essential insights for the optimization of deep mine geothermal systems and supports effective decision-making.