Shape memory polymer (SMP) epoxy composites have attracted significant attention due to their easy processing, lightweight nature, and ability to recover strain. However, their limited recovery rate and inferior mechanical properties have hindered their functional applications. This research explores the potential of three-dimensional (3D) graphene foam (GrF) as a highly efficient reinforcement for SMP epoxy composites. We demonstrated that the incorporation of a mere 0.13 wt.% GrF into mold-cast SMP epoxy leads to a 19% increase in the glass transition temperature (Tg). To elucidate the reinforcing mechanism, we fabricated and extensively analyzed composites with varying weight percentages of GrF. The GrF-based SMP epoxy composite exhibits a 57% increase in thermal conductivity, measuring 0.296 W mK−1 at 70 °C, due to the interconnected 3D graphene network within the matrix. Notably, this composite also demonstrates remarkable electrical conductivity, making it suitable for dual-triggering applications. The GrF-SMP epoxy composite achieves a maximum shape recovery ratio and a significant 23% improvement in the recovery rate, effectively addressing the issue of slow recovery associated with SMPs. We investigated the effect of switching temperatures on the shape recovery rate. We identified the optimal triggering temperature to initiate shape recovery for epoxy SMP and GrF-epoxy SMP as thermal energy equivalent to Tg + 20 °C. Additionally, we fabricated a bird-shaped composite using GrF reinforcement, which showcases self-healing capabilities through the crack opening and closure and serves as a tangible demonstration of the transformative potential of the composite. These GrF-epoxy SMP composites, responsive to stimuli, hold immense promise for diverse applications, such as mechanical systems, wearable sensors, morphing wings, foldable robots, and antennas.