Accurate and efficient brain tumor segmentation remains a critical challenge in neuroimaging due to the heterogeneous nature of tumor subregions and the high computational cost of volumetric inference. In this paper, we propose EfficientGFormer, a novel architecture that integrates pretrained foundation models with graph-based reasoning and lightweight efficiency mechanisms for robust 3D brain tumor segmentation. Our framework leverages nnFormer as a modality-aware encoder, transforming multi-modal MRI volumes into patch-level embeddings. These features are structured into a dual-edge graph that captures both spatial adjacency and semantic similarity. A pruned, edge-type-aware Graph Attention Network (GAT) enables efficient relational reasoning across tumor subregions, while a distillation module transfers knowledge from a full-capacity teacher to a compact student model for real-time deployment. Experiments on the MSD Task01 and BraTS 2021 datasets demonstrate that EfficientGFormer achieves state-of-the-art accuracy with significantly reduced memory and inference time, outperforming recent transformer-based and graph-based baselines. This work offers a clinically viable solution for fast and accurate volumetric tumor delineation, combining scalability, interpretability, and generalization.