Deep-learning-based super-resolution methods have been extensively studied and achieved significant performance with deep convolutional neural networks. However, the results still suffer from the ringing effect, especially in satellite image super-resolution tasks, due to the loss of image details in the satellite degradation process. In this paper, we build a novel satellite super-resolution framework by decomposing a high-resolution image into three components, i.e., low-resolution, artifact, and high-frequency information. Specifically, we propose an artifact removal network with a self-adaption difference convolution (SDC) to fully exploit the structure prior in the low-resolution image and predict the artifact map. Considering that the artifact map and the high-frequency map share a similar pattern, we introduce the supervised structure correction block (SSC) that establishes a bridge between the high-frequency generation process and the artifact removal process. Experimental results on satellite images demonstrate that the proposed method owns an improved tradeoff between the performance and the computational cost compared to existing state-of-the-art satellite and natural super-resolution methods. The source code is available at https://github.com/jiaming-wang/ARSRN.