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Human pose sequence refinement plays a crucial role in improving the temporal coherence of pose estimation across the sequence of frames. Despite its importance in real-world applications, human pose sequence refinement has received less attention than human pose estimation. In this paper, we propose PS-Mamba, a novel framework that refines human pose sequences by integrating spatial-temporal graph learning with state space modeling. Specifically, we introduce the Spatial-Temporal Graph State Space (ST-GSS) block, which captures spatial and temporal dependencies across joints to smooth pose sequences while preserving structural integrity. The spatial-temporal graph learns intricate joint interactions, while the state space component effectively manages temporal dynamics, reducing both short- and long-term pose instability. Besides, we incorporate a dynamic graph weight matrix to adaptively model the relative influence of joint interactions, further mitigating pose ambiguity. Experiments on challenging benchmarks show that our PS-Mamba outperforms SOTAs, achieving -14.21 mm MPJPE (+18.5%\uparrow), -13.59 mm PA-MPJPE (+22.1%\uparrow), and -0.42 mm/s2 ACCEL (+9.7%\uparrow) compared to SynSP on AIST++, significantly reducing jitters and enhancing pose stability.