Geothermal energy, representing one of the five principal non-carbon-based renewable resources, is crucial in the global energy transition and in mitigating greenhouse gas emissions. Hot Dry Rock (HDR) reservoirs, rich in geothermal resources, predominantly utilize hydraulic fracturing, the most extensively researched and applied technology. However, fracturing these robust HDR formations poses significant challenges compared to traditional hydraulic fracturing in sedimentary rocks in the oil and gas industry. Cyclic pulse fracturing, an innovative mode of fracturing, has received limited academic attention, particularly regarding its permeability enhancement mechanism under varying thermal and pressure conditions, which remains largely unexplored. Building on prior laboratory experiments, this study employs the pore pressure cohesive zone model within ABAQUS software to elucidate the initiation and expansion of hydraulic fractures. Numerical simulations investigated the influence of critical parameters such as pulse pattern, temperature, geostress differential, and confining pressure on fracture propagation. The findings indicate that cyclic pulse hydraulic fracturing can significantly reduce the breakdown pressure in HDR, with reductions up to 37.68% under certain conditions. Notably, at constant amplitude, increased frequency exacerbates damage to hot dry rocks; conversely, at constant frequency, higher amplitudes result in greater damage. Additionally, pulse hydraulic fracturing improves the fracturing process, yielding a more intricate fracture network. In HDR pulse hydraulic fracturing, the temperature disparity between the fracturing fluid and the rock markedly impacts the breakdown pressure. Cold water interacting with a high-temperature geo-thermal reservoir triggers a thermal shock effect, diminishing initiation pressure and expediting fracture development and expansion. The impact of geostress differential and confining pressure on pulse hydraulic fracturing is complex, influencing not only the breakdown pressure but also the direction and extent of fracture expansion.