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Mining spatiotemporal mobility patterns is crucial for optimizing urban planning, enhancing transportation systems, and improving public safety by providing useful insights into human movement and behavior over space and time. As an unsupervised learning technique, time series clustering has gained considerable attention due to its efficiency. However, the existing literature has often overlooked the inherent characteristics of mobility data, including high-dimensionality, noise, outliers, and time distortions. This oversight can lead to potentially large computational costs and inaccurate patterns. To address these challenges, this paper proposes a novel neural network-based method integrating temporal autoencoder and dynamic time warping-based K-means clustering algorithm to mutually promote each other for mining spatiotemporal mobility patterns. Comparative results showed that our proposed method outperformed several time series clustering techniques in accurately identifying mobility patterns on both synthetic and real-world data, which provides a reliable foundation for data-driven decision-making. Furthermore, we applied the method to monthly county-level mobility data during the COVID-19 pandemic in the U.S., revealing significant differences in mobility changes between rural and urban areas, as well as the impact of public response and health considerations on mobility patterns.