Based on the measurements of the spilt Hopkinson pressure bar (SHPB) dynamic tests on the jointed rock mass, we analyze the influence of various factors on the jointed rock mass, including the joint plane angle, penetration degree, thickness, crack group number, fillers and strain rate. By analyzing the mechanism of damage and the mode of failure for the jointed rock mass under high-strain rate, the general Bingham model is modified based on the theory of composite damage, and a constitutive model for modelling the dynamic response of the jointed rock mass under different strain rates is developed. Comparison of the theoretical simulations with the experimental results shows that the model can well describe the stress-strain relationship of the jointed rock mass in the early stage of elastic deformation, the steady stage of plastic deformation and the destruction stage of accelerating deformation under dynamic loading. The theoretical results agree well with the experimental data, showing the capability and good performance of the proposed constitutive model.