One of the main reasons for Alzheimer's disease (AD) is the disorder of some neural circuits. Existing methods for AD prediction have achieved great success, however, detecting abnormal neural circuits from the perspective of brain networks is still a big challenge. In this work, a novel decoupling generative adversarial network (DecGAN) is proposed to detect abnormal neural circuits for AD. Concretely, a decoupling module is designed to decompose a brain network into two parts: one part is composed of a few sparse graphs which represent the neural circuits largely determining the development of AD; the other part is a supplement graph, whose influence on AD can be ignored. Furthermore, the adversarial strategy is utilized to guide the decoupling module to extract the feature more related to AD. Meanwhile, by encoding the detected neural circuits to hypergraph data, an analytic module associated with the hyperedge neurons algorithm is designed to identify the neural circuits. More importantly, a novel sparse capacity loss based on the spatial-spectral hypergraph similarity is developed to minimize the intrinsic topological distribution of neural circuits, which can significantly improve the accuracy and robustness of the proposed model. Experimental results demonstrate that the proposed model can effectively detect the abnormal neural circuits at different stages of AD, which is helpful for pathological study and early treatment.