Axial Seamount, an extensively instrumented submarine volcano, lies at the intersection of the Cobb-Eickelberg hot spot and the Juan de Fuca Ridge. Since late 2014, the Ocean Observatories Initiative (OOI) has operated a seven-station cabled ocean bottom seismometers (OBS) array that captured Axial's last eruption in April 2015. This network streams data in real-time, facilitating seismic monitoring and analysis for volcanic unrest detection and eruption forecasting. In this study, we introduce a machine learning (ML) based real-time seismic monitoring framework for Axial Seamount. Combining both supervised and unsupervised ML and double-difference techniques, we constructed a comprehensive, high-resolution earthquake catalog and effectively discriminated between various seismic and acoustic events. These signals include earthquakes generated by different physical processes, acoustic signals of lava-water interaction, and oceanic sources such as whale calls. We first built a labeled ML-based earthquake catalog that extends from November 2014 to the end of 2021, and then implemented real-time monitoring and seismic analysis starting in 2022. With rapid determination of high-resolution earthquake locations and the capability to track potential precursory signals and co-eruption indicators of magma outflow, this system may improve eruption forecasting by providing short-term constraints on Axial's next eruption. Furthermore, our work demonstrated an effective application that integrates unsupervised learning for signal discrimination in real-time operation, which could be generalized to other regions for volcanic unrest detection and enhanced eruption forecasting.