The large-scale implementation of municipal solid waste incineration (MSWI) has put great pressure on waste management and environmental protection. Road construction engineering has also been confronted with the challenges of the heavy consumption of non-renewable mineral resources. Therefore, we evaluated the feasibility of recycling and reusing MSWI residue as an alternative to limestone filler (LF) in transport infrastructure. We investigated the rheological characteristics and fatigue performance of asphalt mastics and mixtures containing MSWI residue. Firstly, a particle size analyzer and environmental scanning electron microscope were adopted to characterize the particle distribution and surface micromorphology of the investigated fillers, respectively. Then, tests for determining the steady shear viscosity and multiple-stress creep recovery were conducted to evaluate the high-temperature rheology of five asphalt mastics. Meanwhile, we used Burgers models with fitting parameters to describe the classic creep recovery measurements and viscoelastic responses. The wheel-tracking test revealed the rutting resistance, and the linear amplitude sweep (LAS) and time sweep tests were combined to investigate the fatigue performances of the five asphalt mastics. A dynamic creep test identified the fatigue life of the asphalt mixtures according to the flow number index. Finally, statistical analysis was conducted to identify the correlations between the rheological and fatigue properties of the mastics and mixtures (R2 over 0.87 and 0.78, respectively). Since the fatigue life predictions for the asphalt mastic decreased by over 42.9% according to the MSWI residue/LF volume ratio, the results of the correlations could improve pavement designs. The substitution of the mineral filler in asphalt mixtures with MSWI residue could be a sustainable strategy for the road construction sector.