Whistle classification plays an essential role in studying the habitat and social behaviours of cetaceans. We obtained six categories of sweep whistles of two Tursiops aduncus individual signals using the passive acoustic mornitoring technique over a period of eight months in the Xiamen area. First, we propose a depthwise separable convolutional neural network for whistle classification. The proposed model adopts the depthwise convolution combined with the followed point-by-point convolution instead of the conventional convolution. As a result, it brings a better classification performance in sample sets with relatively independent features between different channels. Meanwhile, it leads to less computational complexity and fewer model parameters. Second, in order to solve the problem of an imbalance in the number of samples under each whistle category, we propose a random series method with five audio augmentation algorithms. The generalization ability of the trained model was improved by using an opening probability for each algorithm and the random selection of each augmentation factor within specific ranges. Finally, we explore the effect of the proposed augmentation method on the performance of our proposed architecture and find that it enhances the accuracy up to 98.53% for the classification of Tursiops aduncus whistles.