Hydrothermal energy exploitation in underground mines offers a promising approach to mitigate water inrush risk and facilitate geothermal energy utilization. Long-term geothermal water extraction induces coupled hydraulic erosion and damage effects that significantly affect borehole stability and threaten the safe and efficient operation of hydrothermal exploitation systems. To investigate the instability mechanism of boreholes during extraction, a coupled hydraulic erosion–damage model is developed based on the mass conservation equation, erosion constitutive relation, and Brinkman equation. This model is validated against laboratory tests and subsequently used to simulate the hydraulic and damage evolution around the borehole. Simulation results show that hydraulic erosion initiates at fracture boundaries, leading to porosity increases, and the regions of elevated porosity, flow velocity, and volume fraction of fluidized particles expand axially into the rock mass, with faster progression near the borehole wall. A damage-based instability criterion is proposed based on quantitative evaluation of the damaged zone evolution, which exhibits exponential growth with time. Sensitivity analyses show that reduced in-situ stress, increased extraction pressure, and larger borehole radius accelerate damage propagation, resulting in earlier onset of borehole instability. Finally, to enhance long-term borehole stability, pre-grouting in the drilling area and regular reinforcement of the borehole wall are recommended, especially under low in-situ stress, high extraction pressure, or large borehole radius.