Aiming at the difficulty of penetration in hard-plasticity formation represented by the Mahu oil field, a new type of chord-edge cutter is proposed. Through theoretical derivation and quantitative analysis of specific unit pressure (SUP) and breaking area, the penetration and rock-breaking area of the chord-edge cutter are studied, which clarifies that the rock-breaking efficiency of the chord-edge cutter is higher than that of the conventional cutter. The first part of the laboratory experiment investigated the drilling efficiency of two mini-bits on a special sample. The results show that the chord-edge cutter mini-bit has higher efficiency than a conventional mini-bit. The second part of the laboratory experiment investigated the influence of rate of penetration (ROP), revolutions per minute (RPM), and rock types on the drilling performance of chord-edge cutter mini-bit. The data show that the chord-edge cutter is more suitable for drilling hard-plastic rocks. It also reveals that the higher the RPM, the lower the stick/slip vibration, but the RPM above a certain value will lead to an increase in lateral vibration. ROP and weight on bit (WOB) are positively correlated. And the higher the drilling speed, the higher the stick/slip vibration and lateral vibration. To verify these conclusions, a field test is carried out in the hard-plastic formation of a well in the Mahu. In this test, compared with a conventional polycrystalline diamond compact (PDC) bit, a roller-cone bit, and a hybrid bit, the chord-edge cutter bit has the best drilling effect. Further, it is found that when using the chord-edge cutter bit, the high RPM and proper control of WOB can achieve a better drilling efficiency. This rule is mutually confirmed with the conclusion of the laboratory experiment. After the above research and its implementation, it can be concluded that the novel chord-edge cutter bit can achieve the research goal of higher efficiency, which provides a new idea to overcome challenges in the hard-plastic strata.