To investigate the influence of intersection structures on the mechanical properties and failure mechanisms of rock materials, a series of uniaxial compression tests on complete red sandstone specimens and specimens with various hole shapes (T-shape, cross-shape, and shaft-roadway-shape) were conducted by the Instron 1346 servo-controlled rock mechanics testing machine. Flac3D software and digital image correlation (DIC) were used to simulate the internal stress distribution of rock specimens and reproduce the process of fracture, i.e., cracks initiate, propagate, and coalesce with each other into macroscopic failure under progressive loading. The results show that the intersection structure has a significant weakening effect on the mechanical properties of the rock. The rock strength, elastic modulus, and peak strain of specimens can be ranked as complete specimens > cross-shaped intersection structure specimens > T-shaped intersection structure specimens > shaft-roadway-shaped intersection structure specimens. The energy consumption ratio of the intersection structure specimens before the peak reaches more than 30%, which is approximately twice that of the intact specimens. The brittleness coefficients of the four types of specimens are 0.18, 0.26, 0.21, and 0.20, respectively. The intersection structure specimens induced different degrees of tensile and compressive stress concentration zones on the top and bottom sides of the intersection center point. As a result, initial tensile cracks parallel to the loading direction and shear cracks leading to spalling failure on both sides of the holes were formed. With the increase of the axial stress, secondary tensile cracks extending on the opposite direction appeared at the upper and lower corners of the hole. When the far-field cracks that propagated along the diagonal line coalesced with secondary tensile cracks, macro shear-failure of the specimens appeared. With the increase in axial stress, the principal strain monitored during the fracture process of the specimens gradually increased, then it slowly decreased after the peak. The arched boundary of the T-shaped intersection structure specimen had good stability because of its advantage of suppressing the occurrence of the spalling failure. The shaft-roadway-shaped intersection structure could provide compensation space for the secondary tensile cracks due to the existence of the vertical well. The degree of inhibition of initial tensile cracks was so small that the type of specimens was highly prone to instability or failure.