Quantitative characterization of the dynamic evolution of the pore-fracture system subjected to the variation of in situ stress is critical to the production of crude oil and CO2 sequestration in an ultralow permeability reservoir. Combining the integrated method of low-field nuclear magnetic resonance (NMR) and fractal characterization, the response of the geometry and petrophysical properties of sandstone to the change in confining stress from 0 to 32 MPa was investigated. In addition, a classification criterion for adsorption pore (AP), percolation pore (PP), and migration pore (MP) was proposed. The sizes of AP, PP, and MP were identified by the T-2 spectra of 0-8.40 ms, 8.40-541.59 ms, and >541.59 ms. Compared with the percentage increase of the PP, a decrease in the AP and MP was observed with an increase in confining stress. Compared with the pore fracture of cap rock, reservoir rock, with an incremental PP of approximately 10%, showed a dynamic response to the increase in stress that is characterized by large shrinkage in the AP, slight decrease in the MP, obvious expansion of the PP, and small compressibility of the whole pore-fracture system. Pore fracture was mostly dominated by the AP and PP and had low heterogeneity characterized by low fractal dimension along with low porosity and high connectivity. For cap rock, two-stage heterogeneity for the PP space subjected to the compressing process was observed, and high porosity and low connectivity were presented.