This paper presents a simultaneous localization and mapping (SLAM) system to provide accurate pose estimation and dynamic scene reconstruction. Our approach proposes a Joint Point-Gaussian Splatting representation, which fully integrates the robustness of isotropic feature points in pose estimation and the flexibility of anisotropic 3D Gaussians in scene representation. This system does not need to suppress the anisotropic representation of Gaussian elements, which enables the mapping module to achieve finer scene representation with lower memory consumption. Additionally, in order to enhance the adaptability of the system in dynamic environments, we introduced a dynamic region recognition module and utilized 3D Gaussian Splatting and 4D Gaussian Splatting representations to represent static and dynamic regions respectively. Furthermore, we developed a local map management strategy for Gaussian Splatting mapping, effectively reducing the memory and computational resource usage in the mapping process. Experiments on public datasets demonstrate that our system achieves state-of-the-art tracking and mapping accuracy compared to existing baselines.