Synthetic Aperture Radar (SAR) is the primary equipment used to detect oil slicks on the ocean’s surface. On SAR images, oil spill regions, as well as other places impacted by atmospheric and oceanic phenomena such as rain cells, upwellings, and internal waves, appear as dark spots. Dark spot detection is typically the initial stage in the identification of oil spills. Because the identified dark spots are oil slick candidates, the quality of dark spot segmentation will eventually impact the accuracy of oil slick identification. Although certain sophisticated deep learning approaches employing pixels as primary processing units work well in remote sensing image semantic segmentation, finding some dark patches with weak boundaries and small regions from noisy SAR images remains a significant difficulty. In light of the foregoing, this paper proposes a dark spot detection method based on superpixels and deeper graph convolutional networks (SGDCNs), with superpixels serving as processing units. The contours of dark spots can be better detected after superpixel segmentation, and the noise in the SAR image can also be smoothed. Furthermore, features derived from superpixel regions are more robust than those derived from fixed pixel neighborhoods. Using the support vector machine recursive feature elimination (SVM-RFE) feature selection algorithm, we obtain an excellent subset of superpixel features for segmentation to reduce the learning task difficulty. After that, the SAR images are transformed into graphs with superpixels as nodes, which are fed into the deeper graph convolutional neural network for node classification. SGDCN leverages a differentiable aggregation function to aggregate the node and neighbor features to form more advanced features. To validate our method, we manually annotated six typical large-scale SAR images covering the Baltic Sea and constructed a dark spot detection dataset. The experimental results demonstrate that our proposed SGDCN is robust and effective compared with several competitive baselines. This dataset has been made publicly available along with this paper.