Indentation of rocks by the Polycrystalline Diamond Compact (PDC) cutter has great impacts on the cutting depth. However, a vast majority of previous studies only focused on the rock cutting process. Further insight into the failure characteristics of rocks subjected to PDC cutter indentation is required to optimize the design of PDC bits. In this paper, a set of experiments were conducted to investigate the effects of back rake angles and mechanical properties of rocks on the PDC cutter indentation. Penetration forces and Acoustic Emission (AE) signals were captured to determine rock failure modes (brittle failure or plastic failure), and the three-dimensional profilometer was used to identify the morphology features of penetration pits. Besides, the penetration efficiency and brittle failure index were defined to evaluate the crushing characteristics of rocks during penetration. The results show that plastic failure dominates the indentation process as the back rake angle is smaller than 20°, which significantly limits the growth of penetration depth. Based on the penetration force and the number of AE hit counts, chipping occurs in the indentation process when using the PDC cutter with greater back rake angles (>20°). Such phenomenon can be further confirmed by topography features of penetration pits. Moreover, the position of brittle failure moves from the front to the back of the cutter as the back rake angle exceeds 40°. Compared with granite and sandstone, chipping occurs more easily in the marble, indicating a higher brittle failure index. In conclusion, back rake angle has great effects on the rock cutting process and the indentation of rocks. Our current study is expected to provide theoretical guidance for the cutter layout in PDC bits.