Segregation of waste crumb rubber powder (WR) modified asphalt binders the large-scale application of WR in asphalt. The method of microwave activation combined with chemical activation (KMWR) was proposed to improve storage stability and rheological properties of WR modified asphalt in this work. Storage stability and rheological properties of virgin asphalt, MWR modified asphalt, and KMWR modified asphalt were comparatively studied by the standard segregation test, bending beam rheometer (BBR) test, and dynamic shear rheometer (DSR) test. The effect of composite activation on waste rubber powder particles was studied by Fourier-transform infrared spectroscopy (FT-IR), scanning electron microscope (SEM), and Brunauer–Emmett–Teller (BET) tests. The main results showed that after the physical and chemical composite activation, the storage stability of waste rubber powder modified asphalt was significantly improved, WR modified asphalt had better crack resistance, better rutting resistance, and better fatigue performance. After physical and chemical activation, WR was desulfurized, and a large number of active groups was grafted on the WR particles.