The 3D Gaussian Splatting (3DGS)-based SLAM system has garnered widespread attention due to its excellent performance in real-time high-fidelity rendering. However, in real-world environments with dynamic objects, existing 3DGS-based SLAM systems often face mapping errors and tracking drift issues. To address these problems, we propose GARAD-SLAM, a real-time 3DGS-based SLAM system tailored for dynamic scenes. In terms of tracking, unlike traditional methods, we directly perform dynamic segmentation on Gaussians and map them back to the front-end to obtain dynamic point labels through a Gaussian pyramid network, achieving precise dynamic removal and robust tracking. For mapping, we impose rendering penalties on dynamically labeled Gaussians, which are updated through the network, to avoid irreversible erroneous removal caused by simple pruning. Our results on real-world datasets demonstrate that our method is competitive in tracking compared to baseline methods, generating fewer artifacts and higher-quality reconstructions in rendering.