Deep learning (DL) applied to a device's radio-frequency fingerprint (RFF) has attracted significant attention in physical-layer authentications due to its extraordinary classification performance. Conventional DL-RFF techniques, trained by adopting maximum likelihood estimation (MLE), tend to overfit the channel statistics embedded in the training dataset. This restricts their practical applications as it is challenging to collect sufficient training data capturing the characteristics of all possible wireless channel environments. To address this challenge, we propose a DL framework of disentangled representation learning (DRL) that first learns to factor the input signals into a device-relevant component and a device-irrelevant component via adversarial learning. Then, it synthesizes a set of augmented signals by shuffling these two parts within a given training dataset for training of subsequent RFF extractor. The implicit data augmentation in the proposed framework imposes a regularization on the RFF extractor to avoid the possible overfitting of device-irrelevant channel statistics, without collecting additional data from unknown channels. Experiments validate that the proposed approach, referred to as DR-RFF, outperforms conventional methods in terms of generalizability to unknown complicated propagation environments, e.g., dispersive multipath fading channels, even though all the training data are collected in a simple environment with dominated direct line-of-sight (LoS) propagation paths.