This study proposes the incorporation of waste steel slag and waste rubber into asphalt to prepare asphalt mastic with increased mechanical properties and can thus concurrently limit environmental pollution from these wastes. The surface of crumb rubber (CR) was activated by NaClO and was then treated with KH550 silane coupling modifier. Dynamic shear rheometer (DSR), multi-stress creep recovery (MSCR) and zero shear viscosity (ZSV) tests were applied explore the high temperature performance of asphalt mastic. The performance of asphalt mastic was analyzed by Burgers model, and the enhancement mechanism was analyzed by Fourier transform infra-red (FTIR) spectroscopy, scanning electron microscopy (SEM), energy dispersive X-ray (EDX), fluorescent microscopy (FM), and X-ray diffraction (XRD). Experimental results showed that coupling modified CR improved the complex modulus (G*) and rutting factor (G*/sinδ) and reduced the temperature sensitivity of asphalt mastic. The coupling modified CR increased the elasticity coefficient E1, viscosity coefficient η1, relaxation time η1/E1 and delay time η2/E2 of asphalt mastic by 2.8 times, 3.6 times, 1.3 times and 0.9 times, respectively, while steel slag powder (SSP) further enhanced the mechanical properties of the asphalt mastic. FM test showed that coupling modifier CR promoted the swelling of CR and SBS polymer, and hence resulted in a well-developed cross-linked network structure in the asphalt. The positive effect of SSP on the high temperature properties of asphalt mastic suggests that the use of SSP and CR in pavement engineering provides a sustainable solution for the disposal of industrial wastes and the preparation of new asphalt mastic with higher mechanical and thermal properties for practical applications.