Brain connectivity alterations associated with mental disorders have been widely reported in both functional MRI (fMRI) and diffusion MRI (dMRI). However, extracting useful information from the vast amount of information afforded by brain networks remains a great challenge. Capturing network topology, graph convolutional networks (GCNs) have demonstrated to be superior in learning network representations tailored for identifying specific brain disorders. Existing graph construction techniques generally rely on a specific brain parcellation to define regions-of-interest (ROIs) to construct networks, often limiting the analysis into a single spatial scale. In addition, most methods focus on the pairwise relationships between the ROIs and ignore high-order associations between subjects. In this letter, we propose a mutual multi-scale triplet graph convolutional network (MMTGCN) to analyze functional and structural connectivity for brain disorder diagnosis. We first employ several templates with different scales of ROI parcellation to construct coarse-to-fine brain connectivity networks for each subject. Then, a triplet GCN (TGCN) module is developed to learn functional/structural representations of brain connectivity networks at each scale, with the triplet relationship among subjects explicitly incorporated into the learning process. Finally, we propose a template mutual learning strategy to train different scale TGCNs collaboratively for disease classification. Experimental results on 1,160 subjects from three datasets with fMRI or dMRI data demonstrate that our MMTGCN outperforms several state-of-the-art methods in identifying three types of brain disorders.