Structured artifacts are semi-regular, repetitive patterns that closely intertwine with genuine image content, making their removal highly challenging. In this paper, we introduce the Scale-Adaptive Deformable Transformer, an network architecture specifically designed to eliminate such artifacts from images. The proposed network features two key components: a scale-enhanced deformable convolution module for modeling local patterns with varying sizes, orientations, and distortions, and a scale-adaptive deformable attention mechanism for capturing long-range relationships among repetitive patterns with different sizes and non-uniform spatial distributions. Extensive experiments show that our network consistently outperforms state-of-the-art methods in several structured artifact removal tasks, including image deraining, image demoir\'eing, and image debanding.