With the continuous proliferation of satellites, accurately determining their operational status is crucial for satellite design and on-orbit anomaly detection. However, existing research overlooks this crucial aspect, falling short in its analysis. Through an analysis of real-time satellite telemetry data, this paper pioneers the introduction of four distinct operational states within satellite attitude control systems and explores the challenges associated with their classification and prediction. Considering skewed data and dimensionality, we propose the Two-Step Graph Convolutional Neural Network (TS-GCN) framework, integrating resampling and a streamlined architecture as the benchmark of the proposed problem. Applying TS-GCN to a specific satellite model yields 98.93% state recognition and 99.13% prediction accuracy. Compared to the Standard GCN, Standard CNN, and ResNet-18, the state recognition accuracy increased by 37.36–75.65%. With fewer parameters, TS-GCN suits on-orbit deployment, enhancing assessment and anomaly detection.