Asphalt modified by microwave-treatment crumb rubber (CR-microwave) and that of deodorant-addition crumb rubber (CR-deodorant) have low unfavorable or detrimental emissions, but their high- and low-temperature performances have been insufficiently researched, potentially limiting their application and promotion. In order to investigate high-temperature performances of the two low-emissions crumb rubber modified asphalt (CRMA), viscosity, temperature ramp, creep and creep recovery and amplitude sweep tests were conducted using Brookfield Viscometer and dynamic shear rheometer (DSR). Also, low-temperature performances of CMRA were characterised by bending beam rheometer (BBR) tests. Results showed that deodorant-addition CR with a high dosage is not allowed considering asphalt workability, but microwave-treatment CR with various dosages can still meet workability requirements. Moreover, the introduction of microwave-treatment CR or deodorant-addition CR into asphalt improved high-temperature performances of asphalt, while the former had lower positive effects on high-temperature performance grades, elastic recovery and deformation resistance of asphalt. Furthermore, like common CRMA, the two low-emissions CRMA had different viscoelastic behaviour from styrene–butadiene-styrene copolymer (SBS) modified asphalt. Additionally, 18% CR-microwave or CR-deodorant can basically improve the low-temperature performance grades of asphalt. Comprehensively considering the workability and high- and low-temperature performances of the two low-emissions CRMA, 18% CR-microwave is recommended for low-emissions CRMA manufacture.