This study investigates the rutting performance of Stone Mastic Asphalt (SMA) mixtures incorporating Reclaimed Asphalt Pavement (RAP) and Warm Mix Asphalt (WMA) additives, with a specific focus on the influence of wheel tracking speed under controlled loading conditions. Two SMA gradations were examined: SMA-1 with cellulose fiber and SMA-2 with coconut fiber as the stabilizing agent. The use of coconut fiber was explored as a sustainable alternative to cellulose, aiming to reduce environmental impact while maintaining mechanical stability. RAP content was varied from 40–60%, while WMA additives Zycotherm (0.05–0.15%) and Wetbond (0.3–0.7%) were employed to reduce production temperatures and enhance binder–aggregate adhesion. Marshall mixes design determined the optimum binder content (OBC) for each blend, and Immersion Wheel Tracking Tests were conducted at tire pressure of 1160 kN/m² and wheel speeds of 20, 25, and 30 passes/min to evaluate rutting characteristics. Statistical analysis using ANOVA validated the significance of the observed trends. Results indicated that the SMA-2 mix with 50% RAP and 0.7% Wetbond exhibited the lowest rut depth and highest rutting resistance, outperforming the cellulose fiber mix in both elastic and plastic deformation control. The incorporation of RAP and WMA reduced virgin aggregate demand, lowered mixing and compaction temperatures, and enhanced sustainability by utilizing locally available coconut fibers to prevent binder draindown. The findings demonstrate that optimized RAP WMA–fiber combinations can produce durable and environmentally responsible SMA pavements, making them highly suitable for high-traffic and heavy-load roadways.