Multi-view clustering (MVC) has emerged as an important unsupervised multi-view learning method that leverages consistent and complementary information to enhance clustering performance. Recently, tensorized MVC, which processes multi-view data as a tensor to capture their cross-view information, has received considerable attention. However, existing tensorized MVC methods generally overlook deep structures within each view and rely on post-processing to derive clustering results, leading to potential information loss and degraded performance. To address these issues, we develop Tensorial Multi-view Clustering with Deep Anchor Graph Projection (TMVC-DAGP), which performs deep projection on the anchor graph, thus improving model scalability. Besides, we utilize a sparsity regularization to eliminate the redundancy and enforce the projected anchor graph to retain a clear clustering structure. Furthermore, TMVC-DAGP leverages weighted Tensor Schatten $p$-norm to exploit the consistent and complementary information. Extensive experiments on multiple datasets demonstrate TMVC-DAGP's effectiveness and superiority.