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The coarse aggregate–mortar interface transition zone (ITZ) has a great influence on the mechanical properties of concrete, which cannot be easily studied using laboratory tests in the mesoscale. In this paper, a series of axial compression tests were conducted using the discrete element method (DEM) on concrete specimens for four phases: coarse aggregates, mortars, aggregate–mortar interface transition zones, and voids. The effects of ITZ strength on macroscopic stress and microscopic cracks under different strength reduction factors were investigated through axial compression testing. With the increase in interface transition strength, the compressive strength of the concrete becomes stronger; moreover, the number of cracks decreases, and the anisotropy of contact orientation becomes weaker. Meanwhile, the direction of crack development and the damage mode of compressed concrete specimens were also dependent on the coarse aggregate–mortar interface strength coefficient.