Colorectal cancer (CRC) accounts for approximately 9.4% of global cancer-related deaths, underscoring the vital role of early detection and polyp removal via colonoscopy to reduce mortality. However, achieving high-precision polyp segmentation is challenging due to the morphological diversity of polyps, boundary ambiguity, and artifacts in endoscopic imaging. To address these challenges, we propose the Reverse Attention Pyramid Transformer (RAPT), a novel network architecture that leverages a pyramid transformer for multi-scale feature extraction, refines polyp boundaries through a reverse attention mechanism, and enhances feature representation via global-local context fusion to jointly optimize segmentation performance and minimize false positives. Extensive evaluations on five public polyp segmentation datasets (Kvasir, CVC-ClinicDB, ETIS, CVC-ColonDB, and CVC-300) demonstrate that RAPT achieves state-of-the-art performance. Notably, on the ETIS dataset, it achieves a mean Intersection over Union (mIoU) of 76.8%, exceeding the previous best result by 2.2 percentage points. The robustness of RAPT in handling complex colonoscopy images highlights its potential for real-world clinical applications. The code is available at GitHub.