Under the conditions of drilling in gravel-bearing and heterogeneous stratas, the movement and force of the PDC bit during drilling are highly unstable. Irregular impact loads often cause fatigue failures such as tooth fracture, tooth breakage and delamination of the composite sheet. Dynamic impact load is the main cause of fatigue failure of cutting-tooth, which seriously affects the rock-breaking performance of PDC bits. This paper proposes a flexible cutting tooth unit consisting of a central tooth, an elastic element, and a base. The technical concept of flexible-cutting rock breaking is to reduce the impact load amplitude suffered during the cutting process to a certain threshold range by setting elastic elements or reducing the support stiffness of the cutting tooth, so as to inhibit the expansion of micro defects caused by the impact dynamic load of cutting teeth and prolong the service life of drill bits. The finite-element models of flexible cutting teeth for rock cutting were established. The influence of cutting depth, front rake angle and stiffness of elastic elements on the cushioning and vibration-absorption effect of flexible cutting was analysed. The results show that flexible cutting can reduce the peak and average value of von Mises stress at the cutting edge. Under different cutting-depth conditions, the decline rates were 21.45−49.02% and 9.42−17.8%, respectively. Then, under different front-rake-angle conditions, the decline rates were 20.51−24.02% and 9.41−17.8%, respectively. There is a suitable stiffness of the elastic element, which makes the peak and average value of von Mises stress at the cutting edge of the flexible cutting-tooth unit perform better and the effect of improving the uneven stress distribution at the cutting edge better. Flexible cutting technology can effectively improve the adaptability of the PDC bit in heterogeneous formations and reduce the occurrence of abnormal failure of cutting teeth. The research results of this paper can provide theoretical support for the drilling speed of PDC bits in hard formations.