Test-time adaptation (TTA) is crucial for mitigating performance degradation caused by distribution shifts in 3D point cloud classification. In this work, we introduce Token Purging (PG), a novel backpropagation-free approach that removes tokens highly affected by domain shifts before they reach attention layers. Unlike existing TTA methods, PG operates at the token level, ensuring robust adaptation without iterative updates. We propose two variants: PG-SP, which leverages source statistics, and PG-SF, a fully source-free version relying on CLS-token-driven adaptation. Extensive evaluations on ModelNet40-C, ShapeNet-C, and ScanObjectNN-C demonstrate that PG-SP achieves an average of +10.3\% higher accuracy than state-of-the-art backpropagation-free methods, while PG-SF sets new benchmarks for source-free adaptation. Moreover, PG is 12.4× faster and 5.5× more memory efficient than our baseline, making it suitable for real-world deployment.