In order to quantitatively investigate the energy dissipation characteristic during the dynamic tension failure of rock materials, the dynamic Brazilian disc tests on red sandstone were conducted using the split Hopkinson pressure bar (SHPB) setup. The states of the specimens after different incident energies can be divided into three forms (i.e., the unruptured state, the ruptured state, and the broken state), and the failure processes of the specimens were recorded by using a high-speed camera. The results show that the ruptured state of the specimen corresponds to the critical failure strain. Taking the critical incident energy as a turning point, two positive linear fitting relations between the dissipated energy and incident energy before and after the point are obtained, and the dynamic linear dissipation law is found. When the incident energy is less than the critical energy, specimens were unruptured after impact. When the incident energy is greater than the critical energy, specimens will be broken after impact. According to the obtained linear energy dissipation law, the dynamic tensile energy dissipation coefficient (DTEDC) was introduced for quantitatively describing the dynamic energy dissipation capacity of rock materials in the dynamic Brazilian disc test. When the specimen is in the unruptured state, the ideal DTEDC is a constant value. When the specimen is in a broken state, the DTEDC increases with the increase of incident energy.