With the widespread development of the quantified-self movement, an increasing number of users rely on mobile applications to monitor their physical activity through their smartphones. However, granting applications a direct access to sensor data exposes users to privacy risks. In particular, motion sensor data are usually transmitted to analytics applications hosted in the cloud, which leverages on machine learning models to provide feedback on their activity status to users. In this setting, nothing prevents the service provider to infer private and sensitive information about a user such as health or demographic attributes. To address this issue, we propose DySan, a privacy-preserving framework to sanitize motion sensor data against unwanted sensitive inferences (i.e., improving privacy) while limiting the loss of accuracy on the physical activity monitoring (i.e., maintaining data utility). Our approach is inspired from the framework of Generative Adversarial Networks to sanitize the sensor data for the purpose of ensuring a good trade-off between utility and privacy. More precisely, by learning in a competitive manner several networks, DySan is able to build models that sanitize motion data against inferences on a specified sensitive attribute (e.g., gender) while maintaining an accurate activity recognition. DySan builds various sanitizing models, characterized by different sets of hyperparameters in the global loss function, to propose a transfer learning scheme over time by dynamically selecting the model which provides the best utility and privacy trade-off according to the incoming data. Experiments conducted on real datasets demonstrate that DySan can drastically limit the gender inference up to 41% (from 98% with raw data to 57% with sanitized data) while only reducing the accuracy of activity recognition by 3% (from 95% with raw data to 92% with sanitized data).