Over the past few years, multiview attributed graph clustering has achieved promising performance via various data augmentation strategies. However, we observe that the aggregation of node information in multilayer graph autoencoder (GAE) is prone to deviation, especially when edges or node attributes are randomly perturbed. To this end, we innovatively propose a tensor-representation-based multiview attributed graph clustering framework with smooth structure (MV_AGC) to avoid the bias caused by random view construction. Specifically, we first design a novel tensor-product-based high-order graph attention network (GAT) with structural constraints to realize efficient attribute fusion and semantic consistency encoding. By imposing attribute augmentation mechanisms and smooth constraints (SCs) on the proposed high-order graph attention autoencoder simultaneously, MV_AGC effectively eliminates the instability of reconstructed graph structures and learns a more compact node representation during training. In addition, we also theoretically analyze the stronger generality and expressiveness of the proposed tensor-product-based attention mechanism over the classical GAT and establish an intuitive connection between them. Furthermore, to address the performance degradation caused by clustering distribution updating, we further develop a simple yet effective clustering objective function-guided self-optimizing module for the final clustering performance improvement. Experimental results on the six benchmark datasets have demonstrated that our proposed method can achieve state-of-the-art clustering performance.