Mining knowledge from human mobility, such as discriminating motion traces left by different anonymous users, also known as the trajectory-user linking (TUL) problem, is an important task in many applications requiring location-based services (LBSs). However, it inevitably raises an issue that may be aggravated by TUL, i.e., how to defend against location attacks (e.g., deanonymization and location recovery). In this work, we present a Semisupervised Trajectory- User Linking model with Interpretable representation and Gaussian mixture prior (STULIG)-a novel deep probabilistic framework for jointly learning disentangled representation of user trajectories in a semisupervised manner and tackling the location recovery problem. STULIG characterizes multiple latent aspects of human trajectories and their labels into separate latent variables, which can be then used to interpret user check-in styles and improve the performance of trace classification. It can also generate synthetic yet plausible trajectories, thus protecting users' actual locations while preserving the meaningful mobility information for various machine learning tasks. We analyze and evaluate STULIG's ability to learn disentangled representations, discriminating human traces and generating realistic motions on several real-world mobility data sets. As demonstrated by extensive experimental evaluations, in addition to outperforming the state-of-the-art methods, our method provides intuitive explanations of the classification and generation and sheds lights on the interpretable mobility mining.