Speech perception in crowded environments is challenging for hearing-impaired listeners. Assistive hearing devices cannot lower interfering speakers without knowing which speaker the listener is focusing on. One possible solution is auditory attention decoding in which the brainwaves of listeners are compared with sound sources to determine the attended source, which can then be amplified to facilitate hearing. In realistic situations, however, only mixed audio is available. We utilize a novel speech separation algorithm to automatically separate speakers in mixed audio, with no need for the speakers to have prior training. Our results show that auditory attention decoding with automatically separated speakers is as accurate and fast as using clean speech sounds. The proposed method significantly improves the subjective and objective quality of the attended speaker. Our study addresses a major obstacle in actualization of auditory attention decoding that can assist hearing-impaired listeners and reduce listening effort for normal-hearing subjects.