Efficient technology is needed to realise reservoir stimulation for deep geothermal energy exploitation. However, the main control parameters of traditional hydraulic fracturing technology are not clear, as well as their coupling effects; besides, the damage mechanism of novel gas fracturing technology is still not determined, which restricts the mining of hot dry rock resources. Therefore, through a series of true triaxial hydraulic fracturing tests, this paper explores the coupling effect of horizontal stress difference and injection rate on hydraulic fracturing; then, the cohesive element is used to establish hydraulic fracturing and gas fracturing models under the same test conditions. Differences in fracture width and fracture network morphology between the two technologies were compared, and the rock-breaking effects in in-situ reservoirs were analysed. The results show that the breakdown pressure of granite increases gradually with the increase of injection rate, at the small horizontal stress difference; but this trend is opposite at the large horizontal stress difference. Under a higher horizontal stress difference, the increment of the maximum fracture width of gas fracturing becomes larger than that of hydraulic fracturing after increasing the injection rate. When the fracturing cluster spacing is reduced, the fracture width and length of gas fracturing gradually become larger than those of hydraulic fracturing; when the injection rate is increased, the hydraulic fracturing network becomes more complex than gas fracturing. This study can provide useful information for applying hydraulic fracturing and gas fracturing in deep geothermal reservoirs.