Acoustic signals (particularly cavitation acoustic signals) generated during the flood discharge of high dams are highly sensitive to various abnormal situations, whereas weak abnormal signal recognition under strong discharge-noise interference is extremely challenging. Based on the prototype and model experiments, the related abnormal acoustic signals and discharge noise were recorded to construct datasets. Subsequently, using the framework of the deep neural network (DNN) speech enhancement method, a squeeze-and-excitation attention based denoising convolutional neural network (SE-DnCNN) based method for weak abnormal acoustic signal enhancement and recognition was proposed and verified using two case studies of cavitation acoustic signal enhancement and multicategory acoustic signal enhancement and recognition. Compared with the DnCNN method and traditional signal processing methods (such as wavelet, EMD, LMS, and RLS), the proposed method achieved excellent signal enhancement performance after training based on limited prior knowledge of signal and noise. It also demonstrated good generalization ability and robustness in multicategory tasks, which significantly improved the abnormal signal recognition accuracy. This study provides technical support for the practical application of acoustic monitoring based on DNN for safety during the flood discharge of high dams.