Impure salt rock strata are extensively distributed in China, giving them great significance in the study of the physical properties of impure salt rock for the construction of underground gas storage in salt mines. To investigate the confining pressure and impurity effects on the mechanical properties and gas permeability characteristics of salt rock, permeability tests under hydrostatic confining pressure and conventional triaxial compression (CTC), on salt rock samples with different impurity contents, were carried out. The results demonstrate that the confining pressure effects cause an increase in triaxial compression strength, but a decrease in permeability. However, impurity enhances the bearing capacity and permeability of the salt rock; both rock strength and permeability increase with an increase in impurity content. Moreover, the broken salt rock specimens were analyzed after the CTC test using Computed Tomography (CT) equipment. To understand the relationships between pore volume and permeability, considering the confining pressure and impurity effects, the cracks were divided into four groups according to different crack diameter ranges: ~0.05 mm, 0.05–1 mm, 1–10 mm and ~10 mm. The CT analysis results show that while the pore volume of smaller cracks shows an “increasing–decreasing” trend by increasing confining pressure, the pore volume of large cracks gradually decreases, indicating that the rock permeability is highly related to macro-cracks. However, impurity has more complicated implications on rock permeability and cracks, and needs further investigation.