With a small number of training range cells, sparse recovery (SR)-based space–time adaptive processing (STAP) methods can help to suppress clutter and detect targets effectively for airborne radar. However, SR algorithms usually have problems of high computational complexity and parameter-setting difficulties. More importantly, non-ideal factors in practice will lead to the degraded clutter suppression performance of SR-STAP methods. Based on the idea of deep unfolding (DU), a space–time two-dimensional (2D)-decoupled SR network, namely 2DMA-Net, is constructed in this paper to achieve a fast clutter spectrum estimation without complicated parameter tuning. For 2DMA-Net, without using labeled data, a self-supervised training method based on raw radar data is implemented. Then, to filter out the interferences caused by non-ideal factors, a cycle-consistent adversarial network (CycleGAN) is used as the image enhancement process for the clutter spectrum obtained using 2DMA-Net. For CycleGAN, an unsupervised training method based on unpaired data is implemented. Finally, 2DMA-Net and CycleGAN are cascaded to achieve a fast and accurate estimation of the clutter spectrum, resulting in the DU-CG-STAP method with unsupervised learning, as demonstrated in this paper. The simulation results show that, compared to existing typical SR-STAP methods, the proposed method can simultaneously improve clutter suppression performance and reduce computational complexity.