Failure of underground structures, especially intersections, becomes more severe as the depth increases, which poses a new challenge for the safe construction and operation of deep rock engineering. To investigate the mechanical properties and fracture behavior of rock with an intersecting hole under compressive loads, a series of uniaxial compression tests was carried out on cuboid red sandstone specimens containing an intersecting hole with three types of shapes by digital image correlation (DIC) technique. The results showed that the existing hole inside specimens leads to almost a 50% reduction of mechanical parameters from that of intact ones, and this weakening effect is associated with the shapes of holes. Failure of specimens is a progressive process in which cracks, i.e., primary tensile cracks, secondary tensile cracks, and shear cracks, initiate from stress concentration zones, propagate along certain direction, and coalesce with each other into macrofractures. Both the real-time principal strain fields and horizontal displacement fields of specimens under compression could be visually displayed by DIC system, and they were in good consistency in characterizing the fracture behavior. Moreover, the propagation characteristics of primary tensile cracks were studied further by quantitatively analyzing the strain variation during the loading process, and the propagation mechanism of “open-close-reopen” of primary tensile cracks was explained in detail.