Waste poly(ethylene terephthalate) (PET) drinking bottles and end-of-life scrap rubber tires are common municipal solid wastes discarded and produced every day, which are usually disposed of in landfills and stockpiles, occupying a great quantity of land and causing serious environmental issues. This study aims to first turn waste PET into two value-added derived additives under the chemical treatment of two amines, namely triethylenetetramine (TETA) and ethanolamine (EA), respectively, and then adopt them in association with crumb rubber (CR) to modify virgin bitumen for preparing various rubberized asphalt mixtures. Subsequently, the high- and low-temperature properties of the rubberized binder modified by PET additives (PET-TETA and PET-EA) were comparatively characterized through dynamic shear rheometer (DSR) and bending beam rheometer (BBR) tests, while the rutting resistance, fatigue resistance, and dynamic modulus of the further fabricated mixtures were evaluated and validated through mixture tests. The results obtained indicate that 2 wt.% PET-TETA and PET-EA contribute to increase the rutting failure temperature of asphalt rubber from 82.2 °C to 85.5 °C and 84.2 °C, respectively, retaining the high grade of PG 82; the low-temperature grade of asphalt rubber slightly decreased from PG-28 to PG-22 as the additive was added; the rut depth slightly changed from 3.10 mm to nearly 3.70 mm; and PET-TETA exhibits the potential to be capable of extending the fatigue life of asphalt rubber in contrast with PET-EA at different stress levels within 450 kPa. Based on the findings of this study, the developed recycling approach is considered to be applicable to not only alleviate the environmental concerns caused by the landfills and stockpiles of those wastes but also make them valuable for building more durable pavement.