Over-smoothing remains a fundamental challenge in deep Graph Neural Networks (GNNs), where repeated message passing causes node representations to become indistinguishable. While existing solutions, such as residual connections and skip layers, alleviate this issue to some extent, they fail to explicitly model how node representations evolve in a node-specific and progressive manner across layers. Moreover, these methods do not take global information into account, which is also crucial for mitigating the over-smoothing problem. To address the aforementioned issues, in this work, we propose a Dual Mamba-enhanced Graph Convolutional Network (DMbaGCN), which is a novel framework that integrates Mamba into GNNs to address over-smoothing from both local and global perspectives. DMbaGCN consists of two modules: the Local State-Evolution Mamba (LSEMba) for local neighborhood aggregation and utilizing Mamba's selective state space modeling to capture node-specific representation dynamics across layers, and the Global Context-Aware Mamba (GCAMba) that leverages Mamba's global attention capabilities to incorporate global context for each node. By combining these components, DMbaGCN enhances node discriminability in deep GNNs, thereby mitigating over-smoothing. Extensive experiments on multiple benchmarks demonstrate the effectiveness and efficiency of our method.