Based on the discrete element method, the effects of mineral (e.g., feldspar) cleavage angle, confining effect of cleavage angle and cleavage spacing on mechanical properties, micro-cracking process and mechanism of hard rocks, and the resulting problems in engineering were investigated in the present study. Numerical results show that: 1) Mineral cleavage has a significant angle effect. It was found that as the cleavage angle increases from 0° to 90°, the elastic modulus, uniaxial compressive strength and post-peak characteristics of the rock are affected. The total number of trans-granular cracks is obviously affected, which is mainly reflected in that the number of feldspar tensile cracks increases significantly, the number of feldspar shear cracks increases to a maximum at 60° and then decreases, and the number of quartz tensile cracks changes significantly. In general, the number of trans- granular cracks increases, while the number of inter- granular cracks decreases. However, tensile and inter- granular cracking dominates the cracking process. 2) Cleavage effect is affected by confining pressure. The confining pressure will cause the number and proportion of inter- granular cracks and trans- granular cracks to change. However, the confining pressure at different angles has different effects on the number and proportion of inter- granular cracks and trans- granular cracks. 3) As the cleavage spacing increases from 2 mm to 4 mm, the number of trans- granular cracks increases and the number of inter- granular cracks decreases. However, the ratio of total shear and tensile cracks keeps constant, indicating that microscopic tensile and shear cracking mechanisms are almost unaffected. In addition, when the proportion of minerals with cleavage characteristics is high and this kind of mineral also has a significant influence on the rock properties, the influence of cleavage characteristics on rock failures, such as spalling and rockburst, should be given attention.