Resting-state functional magnetic resonance imaging (rs-fMRI) has been widely used in the detection of brain disorders such as autism spectrum disorder based on various machine/deep learning techniques. Learning-based methods typically rely on functional connectivity networks (FCNs) derived from blood-oxygen-level-dependent time series of rs-fMRI data to capture interactions between brain regions-of-interest (ROIs). Graph neural networks have been recently used to extract fMRI features from graph-structured FCNs, but cannot effectively characterize spatiotemporal dynamics of FCNs, e.g., the functional connectivity of brain ROIs is dynamically changing in a short period of time. Also, many studies usually focus on single-scale topology of FCN, thereby ignoring the potential complementary topological information of FCN at different spatial resolutions. To this end, in this paper, we propose a multi-scale dynamic graph learning (MDGL) framework to capture multi-scale spatiotemporal dynamic representations of rs-fMRI data for automated brain disorder diagnosis. The MDGL framework consists of three major components: 1) multi-scale dynamic FCN construction using multiple brain atlases to model multi-scale topological information, 2) multi-scale dynamic graph representation learning to capture spatiotemporal information conveyed in fMRI data, and 3) multi-scale feature fusion and classification. Experimental results on two datasets show that MDGL outperforms several state-of-the-art methods.