Attributed graph clustering, the task of grouping nodes into communities using both graph structure and node attributes, is a fundamental problem in graph analysis. Recent approaches have utilized deep learning for node embedding followed by conventional clustering methods. However, these methods often suffer from the limitations of relying on the original network structure, which may be inadequate for clustering due to sparsity and noise, and using separate approaches that yield suboptimal embeddings for clustering. To address these limitations, we propose a novel method called Deep Attributed Clustering with High-order Proximity Preserve (DAC-HPP) for attributed graph clustering. DAC-HPP leverages an end-to-end deep clustering framework that integrates high-order proximities and fosters structural cohesiveness and attribute homogeneity. We introduce a modified Random Walk with Restart that captures k-order structural and attribute information, enabling the modelling of interactions between network structure and high-order proximities. A consensus matrix representation is constructed by combining diverse proximity measures, and a deep joint clustering approach is employed to leverage the complementary strengths of embedding and clustering. In summary, DAC-HPP offers a unique solution for attributed graph clustering by incorporating high-order proximities and employing an end-to-end deep clustering framework. Extensive experiments demonstrate its effectiveness, showcasing its superiority over existing methods. Evaluation on synthetic and real networks demonstrates that DAC-HPP outperforms seven state-of-the-art approaches, confirming its potential for advancing attributed graph clustering research.