To explore the influence of joint morphology and its degree of anastomosis on the propagation of stress waves, effects of joint matching coefficient (JMC) and its geometric distribution on the dynamic mechanical properties of joints and the propagation of stress waves were analyzed. Cement mortar samples were adopted to prepare cylindrical specimens for simulating rock samples. The distribution pattern of joints was quantified by dividing the end surface of a cylinder into different numbers of fan-shaped concave surfaces. Meanwhile, two specimens with same joint morphology and distribution were obtained at different angles. The split Hopkinson pressure bar (SHPB) was employed for impact test and the results showed that when the joint morphology of the specimens were the same, the nonlinearity of the stress-strain curves in the loading section increased with the increase of the joint contact area. It revealed that the smaller the contact area was, the more obvious the mechanical response of the joint to the initial stage of loading was. Similarly, under the condition of same joint morphology of the composite specimens, the stress wave transmission coefficient and the joint equivalent stiffness increased linearly with the increase of the joint contact area. When the contact area of the joint specimens was the same, the more dispersed the geometric distribution of the joint surface (the more the number of the fan-shaped concave) was, the greater the transmission coefficient and the equivalent stiffness of the stress wave became. The larger the contact area of the joint was, the more obvious the joint geometry distribution effect was.