Unsteady partial cavitation flows are characterized by strong nonlinearity and multi-stage dynamics involving sheet or cloud cavitation inception, development, and collapse, which pose significant challenges for flow analysis and modeling. With the increasing interest in applying machine learning techniques to cavitating flows, data-driven methods provide new opportunities to investigate their complex spatiotemporal behavior beyond traditional linear modal decomposition. In this work, a convolutional neural network-based autoencoder (CNN-AE) is employed to extract nonlinear latent representations of three-dimensional unsteady cavitation flows for flow state identification. We first generated high-resolution flow field data by solving the compressible Euler equations. The trained CNN-AE encodes high-dimensional flow snapshots into a compact latent space, from which spatiotemporal trajectories are constructed to describe the temporal evolution of the cavitation dynamics. Based on these spatiotemporal structures, we apply unsupervised clustering methods to identify distinct cavitation stages. The proposed framework is applied on the 3D-NACA0015 hydrofoil with different cavitation number. The results indicate that the proposed CNN-AE-based framework can effectively distinguish multiple cavitation stages and capture transitional processes between them. Compared with conventional POD-based representations, the learned latent trajectories exhibit enhanced sensitivity to localized small-scale structures and improved separability of transitional cavitation states, which facilitates more robust unsupervised classification. Moreover, the spatiotemporal trajectories obtained by this method provide another perspective for comparing results with different cavitation numbers. The identified flow stages provide physically interpretable labels for unsteady cavitation data, offering a useful foundation for future data-driven modeling and the development of advanced numerical schemes for cavitation flow simulations.