To address the computational redundancy, inadequate multi-scale feature capture, and poor noise robustness of traditional deep networks used for bearing vibration and acoustic signal feature extraction, this paper proposes a fault diagnosis method based on Depthwise Separable Atrous Convolution (DSAC) and Acoustic Spatial Pyramid Pooling (ASPP). First, the Continuous Wavelet Transform (CWT) is applied to the vibration and acoustic signals to convert them into time–frequency representations. The vibration CWT is then fed into a multi-scale feature extraction module to obtain preliminary vibration features, whereas the acoustic CWT is processed by a Deep Residual Shrinkage Network (DRSN). The two feature streams are concatenated in a feature fusion module and subsequently fed into the DSAC and ASPP modules, which together expand the effective receptive field and aggregate multi-scale contextual information. Finally, global pooling followed by a classifier outputs the bearing fault category, enabling high-precision bearing fault identification. Experimental results show that, under both clean data and multiple low signal-to-noise ratio (SNR) noise conditions, the proposed DSAC-ASPP method achieves higher accuracy and lower variance than baselines such as ResNet, VGG, and MobileNet, while requiring fewer parameters and FLOPs and exhibiting superior robustness and deployability.