Mixing multi-source vibration signals presents a major challenge in target recognition in distributed fiber optic acoustic sensor systems. This article proposes a deep learning method for separating ultra-weak fiber Bragg grating (UW-FBG) distributed acoustic sensor (DAS) multi-source signals. An experimental setup is constructed to create vibration environments for knocking, fan vibration, and steel pipe friction. The UW-FBG DAS system is used to collect single-source vibration signals, as well as two-source and three-source mixed vibration signals. First, a wavelet denoising algorithm is used to preprocess the data. Second, the datasets are constructed for simulated mixed signals and measured mixed signals. The Conv-TasNet deep learning network is utilized to separate DAS vibration signals. Results demonstrate that the proposed method can separate mixed signals of vibration, fan, and steel pipe friction sources, obtaining the corresponding time–frequency entropy similarity of 97.5%, 92.8% and 90.2%, and compared with commonly used multi-source signal separation methods, it has advantages in separation performance and separation time, and exhibits good robustness in different signal environments. This finding the efficacy of the separation method and provides a valuable solution for DAS multi-source signal separation problems in complex environments.