<p>The dynamic damage constitutive model has limitations and needs to reflect the quantitative relationship between the elastic modulus and joint inclination angle of the slate. This paper constructs a dynamic damage constitutive model considering the influence of joint inclination on the elastic modulus of slate. First, the slate impact test reveals the changing law of the elastic modulus of slate under different joint inclination angles. The elastic modulus of slate with joint inclination angle shows a “U” type changing law, and the elastic modulus is the smallest when the joint inclination angle is 52.5°, and the elastic modulus is relatively larger when 0° and 90°. The mathematical model of slate joint inclination and elastic modulus was obtained by fitting the test data, and the fitting accuracy reached 94.86%. Then, the dynamic damage constitutive model of slate was established based on the statistical distribution theory, and the quantitative relationship between joint inclination and elastic modulus was introduced into the damage eigen structure equation to correct the elastic modulus. Finally, comparing the theoretical calculations with the experimental results, the stress–strain curves of the slate before damage are in good agreement, proving the model’s rationality in this paper.</p>