In the context of the global pandemic of COVID-19, the use and disposal of medical masks have created a series of ethical and environmental issues. The purpose of this paper is to study and evaluate the high temperature properties and thermal storage stability of discarded-mask (DM)-modified asphalt from a multi-scale perspective using molecular dynamics (MD) simulation and experimental methods. A series of tests was conducted to evaluate the physical, rheological, thermal storage stability and microscopic properties of the samples. These tests include softening point, rotational viscosity, dynamic shear rheology (DSR), Fourier transform infrared (FT-IR) spectroscopy and molecular dynamics simulation. The results showed that the DM modifier could improve the softening point, rotational viscosity and rutting factor of the asphalt. After thermal storage, the DM-modified asphalt produced segregation. The difference in the softening point between the top and bottom of the sample increased from 2.2 °C to 17.1 °C when the DM modifier admixture was increased from 1% to 4%. FT-IR test results showed that the main component of the DM modifier was polypropylene, and the DM-modified asphalt was mainly a physical co-blending process. MD simulation results show that the DM modifier can increase the cohesive energy density (CED) and reduce the fractional free volume (FFV) of asphalt and reduce the binding energy between base asphalt and DM modifier. Multi-scale characterization reveals that DM modifiers can improve the high temperature performance and reduce the thermal storage stability of asphalt. It is noteworthy that both macroscopic tests and microscopic simulations show that 1% is an acceptable dosage level.