Hyperspectral images (HSIs) have unique advantages in distinguishing subtle spectral differences of different materials. However, due to complex and diverse backgrounds, unknown prior knowledge, and imbalanced samples, it is challenging to separate background and anomaly. In this article, we present a novel characterization of background-anomaly separability with a generative adversarial network (BASGAN) for hyperspectral anomaly detection. The key contribution is the proposal to explicitly constrain the background and anomaly separability by characterizing background spectral samples while avoiding anomaly reconstruction. First, we use a class saliency map extraction algorithm to obtain pseudobackground and anomaly samples for adversarial training. To further mitigate the suffering of anomaly contamination in background distribution estimation, we introduce background-anomaly separability constrained loss function to enhance the reconstruction of the background while weakening the anomaly reconstruction in a semisupervised way. Additionally, a discriminator is induced into the latent space to make the encoded representation resemble Gaussian distribution during adversarial training. The other is adversarial training in the reconstruction space so that the background estimation can be improved. Experiments conducted on real data sets illustrate the superior background-anomaly separability of the proposed method.