This paper introduces MipSLAM, a frequency-aware 3D Gaussian Splatting (3DGS) SLAM framework capable of high-fidelity anti-aliased novel view synthesis and robust pose estimation under varying camera configurations. Existing 3DGS-based SLAM systems often suffer from aliasing artifacts and trajectory drift due to inadequate filtering and purely spatial optimization. To overcome these limitations, we propose an Elliptical Adaptive Anti-aliasing (EAA) algorithm that approximates Gaussian contributions via geometry-aware numerical integration, avoiding costly analytic computation. Furthermore, we present a Spectral-Aware Pose Graph Optimization (SA-PGO) module that reformulates trajectory estimation in the frequency domain, effectively suppressing high-frequency noise and drift through graph Laplacian analysis. Extensive evaluations on Replica and TUM datasets demonstrate that MipSLAM achieves state-of-the-art rendering quality and localization accuracy across multiple resolutions. Code is available at https://github.com/yzli1998/MipSLAM.