The issue of forming a reliable and stable structure of a crumb-rubber-modified binder is an important scientific and technical task. The authors supplemented existing concepts of the mechanism of effective interaction with rubber crumb by introducing a preliminary first stage: controlled partial physical destruction of rubber crumb—producing rubber reclaim. Proposed physical methods of rubber crumb destruction include high shear force (roll mills), high temperature, and a plasticizing medium. The controllability and degree of devulcanization of rubber were determined by acetone-chloroform extraction in different time intervals. The degree of devulcanization of rubber in the rubber reclaim was found to be 22 ± 0.24%, with stability over 14 days. It was found that the size of the particles of the rubber reclaim in the bitumen is less than 2 µm. The properties of the structure of the binder modified with rubber reclaim, characterizing the stability and sustainability, have been studied and established. The developed modified binders are stable in storage. Rheological parameters of the structure characterizing intermolecular interaction, such as shear stability for original and RTFOT-aged, modified bitumen, meet requirements of the state standard at test temperature 64 °C. The elastic structural component of the crumb-rubber-modified binder, as indicated by the relative irreversible deformation parameter J3,2, does not exceed 2.6 kPa (<4.5 kPa) at 64 °C. Additionally, it was determined that the rheological structural parameter for fatigue resistance, which characterizes the durability of road pavement under intensive operational conditions, does not exceed 4699 kPa (<5000 kPa) at 16 °C. The use of 10% rubber reclaim combined with waste frying oil provided the opportunity to obtain a modified binder with a stable and sustainable structure without the introduction of additional stabilizers and agents. Test results showed that the overall performance characteristics of the modified binder meet the 64(S)-40 grade standards.