To investigate the influence of microwave heating on the dynamic behavior and failure mechanisms of rock, dynamic compression tests were conducted on microwave-irradiated sandstone specimens using a modified split Hopkinson pressure bar (SHPB) system. Experimental results show that microwave radiation can effectively weaken the compressive strength of sandstone. Rock specimens show three different failure modes under impact load: tensile failure, tensile-shear composite failure and compressive-shear failure. The dynamic Poisson’s ratio, calculated using the measured P- and S-wave velocities, is introduced to describe the deformation characteristics of sandstone. With the increase in microwave power and heating time, the Poisson’s ratio declines first and then increases slightly, and the turning point occurs at 244.6 °C. Moreover, the microstructural characteristics reveal that microwave radiation produces dehydration, pore expansion, and cracking of the rock. The damage mechanisms caused by microwave radiation are discussed based on thermal stress and steam pressure inside the rock, which provides a reasonable explanation for the experimental results.