Hot-dry-rock (HDR) has long been considered a potential exploitable energy source due to its high energy content, cleanliness, and abundant reserves. However, HDR typically resides in ultra-deep strata with high temperatures and pressures, which makes its extraction a highly complex thermal-hydrological-mechanical (THM) coupling. In this paper, the THM coupling relationship in the geothermal extraction is clarified. It establishes a dynamic porosity and permeability model and creates a pair-well geothermal extraction model. The investigation focuses on understanding the influence of the pressure difference between pair-wells, number of cracks, and injection temperature on the heat extraction temperature, permeability ratio, geothermal reservoir reduction rate, and heat extraction temperature. The research findings indicate the following: (1) Increasing the inter-well pressure difference from 2 to 10 MPa reduces the extraction temperature from 155 to 138 °C. However, the thermal reservoir permeability ratio increases from 1.07 to 1.35. Consequently, the extraction efficiency rises from 6.2 to 12.4 MW. (2) The number of cracks from 200 to 400 led to a decrease in extraction temperature from 160 to 115 °C. However, the thermal reservoir permeability ratio increases from 1.12 to 1.35. In the first 8 years of extraction, the thermal pumping power of 400 cracks exceeded 200 cracks, but later this trend reversed. (3) Elevating the injection temperature from 20 to 60 °C increases the extraction temperature from 142 to 158 °C while reducing the permeability ratio from 1.28 to 1.20. Consequently, the extraction power decreases from 8 to 6 MW. (4) The inter-well pressure difference has the greatest impact on the decrease in extraction temperature, whereas the number of cracks has the greatest impact on the increase in permeability ratio. Injection temperature has the most significant impact on extraction power. This study reveals that increasing the pressure difference between wells, increasing the number of cracks, and lowering the injection fluid temperature will enhance geothermal extraction power. These findings provide valuable insights for geothermal development.