Anomaly detection under open-set scenario is a challenging task that requires learning discriminative fine-grained features to detect anomalies that were even unseen during training. As a cheap yet effective approach, data augmentation has been widely used to create pseudo anomalies for better training of such models. Recent wisdom of augmentation methods focuses on generating random pseudo instances that may lead to a mixture of augmented instances with seen anomalies, or out of the typical range of anomalies. To address this issue, we propose a novel saliency-guided data augmentation method, SaliencyCut, to produce pseudo but more common anomalies which tend to stay in the plausible range of anomalies. Furthermore, we deploy a two-head learning strategy consisting of normal and anomaly learning heads, to learn the anomaly score of each sample. Theoretical analyses show that this mechanism offers a more tractable and tighter lower bound of the data log-likelihood. We then design a novel patch-wise residual module in the anomaly learning head to extract and assess the fine-grained anomaly features from each sample, facilitating the learning of discriminative representations of anomaly instances. Extensive experiments conducted on six real-world anomaly detection datasets demonstrate the superiority of our method to competing methods under various settings.