The compatibility of crumb rubber (CR) modified asphalt restricts its application in pavement engineering. In this study, desulfurized (DS) and depolymerized (DP) CR-modified asphalts (CRMA) were prepared, and molecular models were constructed using molecular dynamics (MD). To analyze the effect of desulfurization and depolymerization on CRMA compatibility, rheological properties, storage stability, and morphological characteristics of CRMA, DSCRMA, and DPCRMA were determined and characterized. The interaction mechanism between CR and asphalt was characterized using indicators including binding energy and diffusion coefficient. Dynamic Shear Rheometer (DSR) results showed that desulfurization and depolymerization significantly improved the high-temperature rutting resistance of CR modified asphalt. Storage stability results indicated a softening point difference of 2.1°C for DSCRMA, meeting the standard of less than 2.5°C. Scanning Electron Microscopy (SEM) revealed a decrease in the size of DSCR particles and an increase in roughness and the number of pores. Fluorescence microscopy observed better dispersion of DSCR particles in asphalt, which was consistent with SEM results. MD results indicated an increase in binding energy between DSCR and light components, while diffusion motion was constrained. The interaction capability of DPCR decreased, possibly due to uneven depolymerization accumulation. The study revealed that desulfurization significantly enhances CRMA compatibility, while the degree of CR depolymerization warrants further investigation into its effects on asphalt.