The impact disturbance has an important influence on the safety of underground engineering openings. In this paper, based on the in-situ stress measurement and structural plane investigation, the model of jointed rock roadway was established using the discrete element method (3DEC) to study the instability and failure characteristic of roadway surrounding rock with dominant joint planes under impact disturbance and to further analyze the influence of different buried depths, impact stress wave peaks, and stress wave delays on the stability of the surrounding rock. The results show that the stability of the surrounding rock is poor, and the whole convergence deformation of the surrounding rock occurs under the impact stress wave. There are three failure modes in the surrounding rock: tensile-shear failure, tensile failure, and shear failure. Tensile-shear failure mainly occurs in a small range close to the roof and floor of the roadway and the free surfaces of the two sides, and tensile failure occurs locally, while shear failure mainly occurs along the joint plane outside this range. Moreover, the greater the buried depth and stress wave peak value, the more serious the deformation of the surrounding rock. With the increase of stress wave delay, the deformation of the surrounding rock shows complex characteristics. In addition, the impact failure mechanism of the surrounding rock in jointed rock masses was discussed. The research results have important guiding significance for the prevention and control of underground engineering cavern disasters.