To reveal the dynamic cracking process of deep rock caused by explosive initiation, the mechanical process of rock cracking is theoretically analyzed firstly under the combined action of explosion stress wave and geostress stress. A new crack dynamic driving model (CDD Model) based on the combined coupling effect is established. The feasibility and rationality of it in characterizing the dynamic cracking process are verified with numerical simulation and laboratory test. And the influence of ground stress on dynamic cracking process of presplitting blasting is revealed. The findings show that the dynamic cracking process of presplitting blasting is affected by explosion stress wave, explosive gas pressure, and ground stress. The opening of explosion crack shows a dynamic changing process of first increasing, then decreasing, and finally increasing. For conventional presplitting blasting, when the initial geostress level exceeds 10 ∼ 20 MPa, the stress transient unloading on fracture surface easily leads to the reduction of the explosive fracture opening. And the possibility of secondary opening and expansion of the explosive fracture is reduced. It will limit the driving effect of the subsequent explosion energy on the fracture expansion.