Abstract: The oil and gas stored in deep and ultra-deep carbonate reservoirs is the focus of future exploration and development. Conical PDC (Polycrystalline Diamond Compact) cutter, which is a new kind of PDC cutter, can significantly improve the rate of penetration (ROP) and extend PDC bit life in hard and abrasive formations. However, the breakage characteristics and failure mode of the conical PDC cutter cutting carbonate rock is still masked. In this paper, a series of single-cutter cutting tests were carried out with the conical and conventional PDC cutters. The cutting force, rock-breaking process, surface morphology of cutting grooves and cuttings characteristic were analyzed. Based on the derived formula of the brittle fracture index, the failure model of carbonate rock was quantitatively analyzed under the action of conical and conventional cutter. The results show that the average cutting force of the conical cutter is less than that of the conventional cutter, which means greater stability of the cutting process using the conical cutter. Carbonate rock with calcite as the main component tends to generate blocky rock debris by conical cutter. The height of the cuttings generated by the conical cutter is 0.5 mm higher than that generated by the conventional cutter. The conical cutter exhibits enhanced penetration capabilities within carbonate rock. The accumulation of rock debris in front of the conventional cutter is obvious. Whereas, the conical cutter facilitates the cuttings transport, thereby alleviating drilling stickiness slip. At different cutting depths, the conical cutter consistently causes asymmetric jagged brittle tensile fracture zones on both sides of the cutting groove. Calculations based on the brittle fracture index demonstrate that the brittle fracture index of the conical cutter generally doubles that of the conventional cutter. For carbonate rock, the conical cutter displays superior utilization of brittle fracture abilities. The research findings of this work offer insights into the breakage process and failure mode of carbonate rock by the conical cutter.