Acoustic emission (AE) signals have been widely employed for tracking material properties and structural characteristics. In this study, we aim to analyze the AE signals gathered during a scanning probe lithography process to classify the known microstructure types and discover unknown surface microstructures/anomalies. To achieve this, we developed a Hidden Markov Model to consider the temporal dependency of the high-resolution AE data. Furthermore, we compute the posterior classification probability and the negative likelihood score for microstructure classification and discovery. Subsequently, we present a diagnostic procedure to identify the dominant AE frequencies that allow us to track the microstructural characteristics. Finally, we apply the proposed approach to identify the surface microstructures of additively manufactured Ti-6Al-4V and show that it not only achieved a high classification accuracy (e.g., more than 90%) but also correctly identified the microstructural anomalies that may be subjected further investigation to discover new material phases/properties.