The industrial operation of oxy-fuel metal cutting via gas torches involves tasks such as ignition, preheating, and combustion along the target surface. Automated oxy-fuel cutting systems are exposed to risks and anomalies that can lead to incorrect actions and safety hazards. In this paper, we develop a classifier for online task state estimation to assess the cutting robot's actions, detect anomalies, and reduce the risk of hazards. Using representative footage from our robotic cutting experiments, we curate an image dataset labeled with four types of cutting task states. Using deep learning methods, we design and train a convolutional neural network model for classifying the cutting task state from input images. The classifier architecture is optimized for rapid inferences during online estimation. After evaluation, our classifier achieves an overall accuracy of 93.8 % with high inference speeds on two types of representative hardware. Our ‘Oxy-fuel Cutting Task State’ (OCTS) dataset is available at doi.org/10.5281/zenodo.7734951.