Deep learning models have recently shown great success in classifying epileptic patients using EEG recordings. Unfortunately, classification-based methods lack a sound mechanism to detect the onset of seizure events. In this work, we propose a two-stage framework, SODor, that explicitly models seizure onset through a novel task formulation of subsequence clustering. Given an EEG sequence, the framework first learns a set of second-level embeddings with label supervision. It then employs model-based clustering to explicitly capture long-term temporal dependencies in EEG sequences and identify meaningful subsequences. Epochs within a subsequence share a common cluster assignment (normal or seizure), with cluster or state transitions representing successful onset detections. Extensive experiments on three datasets demonstrate that our method can correct misclassifications, achieving 5\%-11\% classification improvements over other baselines and accurately detecting seizure onsets.