Rotating components, as the core functional part of rotating machinery, their performance directly determines the stability, reliability, and safety of the equipment operation. Effective intelligent fault identification techniques are being developed as a promising tool for perceiving the state of rotating elements. However, the domain shift phenomenon caused by internal and external interference inevitably exists in practical application scenarios, which significantly deteriorates the performances of the intelligent diagnosis model. Besides, most of the existing intelligent fault diagnosis models are constructed mainly for the single task attribute, that is, the established model can only meet the requirements of a single task, such as the identification of different fault severities or the monitoring of different fault locations. To overcome these challenges, a novel multi-task domain adaptation framework, called deep multi-scale separable convolutional network with triple attention mechanism (MSSCN-TAM), is established in this paper. First, the condition monitoring data preprocessed based on Fast Fourier Transform (FFT) is fed into the improved separable convolution (ISC) module, in which depth-attention and point-attention are introduced to make it self-adjusting. Then, combined with the scale-attention mechanism, which determines the contribution of each branch, the output nodes of each ISC module are connected across scales and treated as the common input of the subsequent two task-specific discriminators. Finally, the weighted Multi-Kernel Maximum Mean Discrepancies (MK-MMD) is adopted to the proposed MSSCN-TAM model to align the distribution and extract domain-invariant features. A total of twenty transfer scenarios based on three rotating component datasets are employed for performance validation of the proposed MSSCN-TAM model, and the multi-task cross-domain transfer diagnosis results show that it has superior transferability and stability.