Exploiting geothermal energy using existing deep mining systems streamlines the development of geothermal systems while addressing the cooling needs of deep mines. However, the combined effects of low-temperature and high-pressure injection during geothermal operations adversely impact the stability of deep mine drifts. This makes it crucial to reliably assess the stability of the drifts and ensure the desired temperature evolution near drifts and the production well. In this paper, we investigate the impact of deep geothermal operations on the stability of mine drifts through thermo-hydro-mechanical (THM) numerical modeling. The results show that impact of cold water injection on the stability of the mine is predominantly influenced by thermal effects, in addition to poro-elastic effects. The reduction in temperature and the increase in pore pressure both contribute to a decrease in effective stress, which is detrimental to the drift stability, though the evolution of the different mechanisms differs. Furthermore, we utilize the distance-based generalized sensitivity analysis (DGSA) method to quantify the sensitivity of the THM model parameters (including design parameters and material properties), thereby optimizing the system design. The results show that the distance between the mine system and the geothermal system is the paramount factor influencing the system's response. Other design parameters (injection rate and temperature, well spacing) and material properties (thermal expansion coefficient, permeability, Young's modulus and heat capacity) also hold substantial significance. Conversely, the system's behaviour is not sensitive to parameters such as porosity and thermal conductivity. By analyzing the range of parameters using DGSA, we provide recommendations for optimizing the system. The verification results show that, given favorable geological settings as suggested, rational selection of system design parameters can facilitate efficient geothermal extraction activities in deep mines. This approach finds optimized development options considering uncertainty of the subsurface, offering valuable advice and guidance for decision-making in geothermal production.