In this work, ground tire rubber and styrene–butadiene block copolymer (GTR/SBS) blends at the ratio of 50/50 wt%, with the application of four different SBS copolymer grades (linear and radial) and two types of cross-linking agent (a sulfur-based system and dicumyl peroxide), were prepared by melt compounding. The rheological and cross-linking behavior, physico-mechanical parameters (i.e., tensile properties, abrasion resistance, hardness, swelling degree, and density), thermal stability, and morphology of the prepared materials were characterized. The results showed that the selected SBS copolymers improved the processability of the GTR/SBS blends without any noticeable effects on their cross-linking behavior—which, in turn, was influenced by the type of cross-linking agent used. On the other hand, it was observed that the tensile strength, elongation at break, and abrasion resistance of the GTR/SBS blends cured with the sulfur system (6.1–8.4 MPa, 184–283%, and 235–303 mm3, respectively) were better than those cross-linked by dicumyl peroxide (4.0–7.8 MPa, 80–165%, and 351–414 mm3, respectively). Furthermore, it was found that the SBS copolymers improved the thermal stability of GTR, while the increasing viscosity of the used SBS copolymer also enhanced the interfacial adhesion between the GTR and SBS copolymers, as confirmed by microstructure evaluation.