Rising traffic volume, heavy loads, and construction activities have raised concerns about expansion joint device damage. This study focuses on developing an innovative expansion joint using polymer-modified rubber asphalt as the filling material to enhance its service life. Styrene–butadiene–styrene (SBS) emerged as a suitable modifier for rubber-modified asphalt, significantly improving elasticity and adhesion. Through the strategic combination of 3- and 2-block linear SBS, the elasticity and adhesion properties were significantly improved, resulting in the formulation of a well-suited polymer-modified rubber asphalt binder. The developed asphalt binder exhibits impressive elastic recovery (61.1% to 66.1%), surpassing commercial products, with enhanced constructability and workability (15% to 21% viscosity reduction). The carefully engineered mastic asphalt mixture showcases self-leveling characteristics at a moderate 210 °C, addressing historical constructability challenges. Settlement is 40% less than traditional hot mix asphalt for surface layers, with improved moisture and stripping resistance, enhancing existing asphalt plug joint durability and workability. Collectively, this novel mixture, comprising polymer-modified rubber and mastic asphalt, showcases the potential to enhance the durability of existing asphalt plug joints while ensuring superior constructability and workability.