Hyperspectral anomaly detection has attracted extensive interests for its wide use in military and civilian fields, and three main categories of detection methods have been developed successively over past few decades, including statistical model-based, representation-based, and deep-learning-based methods. Most of these algorithms are essentially trying to construct proper background profiles, which describe the characteristics of background and then identify the pixels that do not conform to the profiles as anomalies. Apparently, the crucial issue is how to build an accurate background profile; however, the background profiles constructed by existing methods are not accurate enough. In this article, a novel and universal background purification framework with extended morphological attribute profiles is proposed. It explores the spatial characteristic of image and removes suspect anomaly pixels from the image to obtain a purified background. Moreover, three detectors with this framework covering different categories are also developed. The experiments implemented on four real hyperspectral images demonstrate that the background purification framework is effective, universal, and suitable. Furthermore, compared with other popular algorithms, the detectors with the framework perform well in terms of accuracy and efficiency.