In recent years, numerous studies have adopted rs-fMRI to construct dynamic functional connectivity networks (DFCNs) and applied them to the diagnosis of brain diseases, such as epilepsy and schizophrenia. Compared with the static brain networks, the DFCNs have a natural advantage in reflecting the process of brain activity due to the time information contained in it. However, most of the current methods for constructing DFCNs fail to aggregate the brain topology structure and temporal variation of the functional architecture associated with brain regions, and often ignore the inherent multi-dimensional feature representation of DFCNs for classification. In order to address these issues, we propose a novel DFCNs construction and representation method and apply it to brain disease diagnosis. Specifically, we fuse the blood oxygen level dependent (BOLD) signal and interactions between brain regions to distinguish the brain topology within each time domain and across different time domains, by embedding block structure in the adjacency matrix. After that, a sparse tensor decomposition method with sparse local structure preserving regularization is developed to extract DFCNs features from a multi-dimensional perspective. Finally, the kernel discriminant analysis is employed to provide the decision result. We validate the proposed method on epilepsy and schizophrenia identification tasks, respectively. The experimental results show that the proposed method outperforms several state-of-the-art methods in the diagnosis of brain diseases.