Sleep stage classification is essential for diagnosing sleep disorders. This work proposes Mamba-CAM-Sleep, a novel framework that utilises the polysomnography (PSG) records and leverages a state-space backbone (Mamba) and channel attention based graph neural network for sleep staging classification. The Mamba backbone enhances long-range temporal dependencies, which is crucial for capturing sleep stage transitions, while channel attention improves discriminative feature extraction across multi-channel signals. The proposed approach is validated on the DOD-H benchmark dataset. The model attains an F1 score of 80.4% and a Cohen's kappa of 76.3%, outperforming existing methods (LSTM, SimpleSleepNet, RobustSleepNet, DeepSleepNet) by 3.0-6.0% and 2.2-10.8% in F1 and kappa, respectively. Notably, our framework demonstrates superior robustness, as evidenced by lower standard deviations (±2.1 F1, ±2.5 kappa), and excels in classifying challenging stages such as N1 (53.9%) and N3 (74.7%), surpassing prior works by 3.3 - 16.5%. Ablation studies validate the effectiveness of the proposed architectural innovations. The proposed Mamba-CAM-Sleep framework is a scalable, reliable solution for clinical sleep staging, striking a balance between high accuracy and practical deployability.