Fractured sandstone is widely distributed in mining areas throughout western China where the artificial freezing method is extensively adopted to construct vertical shafts. Blasting and excavation generate stress waves and break frozen fractured sandstone. Among the failure modes of frozen fractured rocks, tensile failure is very common. In this study, the dynamic tensile strength of fractured sandstone samples with four crack inclination angles (0°, 30°, 60°, and 90°) is tested by using a split Hopkinson pressure bar at four subzero temperatures (−5, −10, −15, and −20°C). Accordingly, a damage constitutive relationship that considers the effect of fissure angle and freezing temperature is established. The results show the following: (1) the fissure angle does not significantly affect the dynamic tensile strength of frozen fractured sandstone but mainly affects the failure mode of the sample. (2) The dynamic tensile strength of fractured sandstone has a negative linear correlation with the freezing temperature. (3) When the fissure angle is small, only tensile cracking occurs; when the fissure angle is large, tensile cracking occurs along both the loading direction and the fissure; and shear cracking occurs along the fissure as well. (4) Regardless of the fissure angle, tensile cracking is initiated at the stress-concentration zone and then propagates towards the loading end. Fissure ice provides both resistance to deformation and resistance to crack propagation which affects the crack propagation and coalescence mode. A dynamic constitutive relationship is established by considering the effects of fissure angle and freezing temperature on the dynamic properties of frozen fractured sandstone, which is proven to be highly reliable and provides a reference and basis to study the dynamic mechanical properties of similar rock types.