The extraction and utilization of non-renewable mineral resources impose significant transportation and economic challenges in infrastructure construction. At the same time, recycling fly ash derived from the bottom ash in municipal solid waste incineration residues (MSWIRs) presents a waste management hurdle. This study investigates the viscoelastic characteristics and mechanical performances at different scales of asphalt mastic and mixture with fly ash from MSWIRs. Firstly, Fourier transform infrared spectrometry (FTIR) was adopted to distinguish the physically blended states of asphalt and fillers. Then, a frequency test using a dynamic shear rheometer (DSR) was conducted to construct viscoelastic master curves, focusing on asphalt mastic. A dynamic modulus test characterized the viscoelastic behavior at the asphalt mixture scale. Furthermore, the mechanical performances of asphalt mixtures were evaluated, including the resilient modulus through indirect tension tests, moisture susceptibility via the immersed Marshall stability test, and anti-cracking properties with a low-temperature bending test. The FA incorporation in the mixture decreased the immersion residual stability by 7.40%, and increased the flexural tensile strength by 5.03% and the stiffness modulus by 78.67%. The mechanical evaluation of the mixture with FA could meet the application requirements of the asphalt layer. Finally, statistical analyses were conducted to present strong correlations (coefficient R2 over 0.70) among the mechanical results. Fly ash in asphalt mixtures revealed potential as a sustainable approach for waste reuse in road construction. Additionally, substituting mineral fillers at the mastic scale significantly influences the viscoelastic characteristics and mechanical performances of asphalt materials at the mixture scale.