The Hall-effect thruster is a prominent space propulsion system, providing a high specific impulse and thrust-to-power ratio. However, detrimental phenomena occurring in Hall thrusters, such as plasma instability and blowoff, are less understood. In this study, we employ a data-driven approach for analyzing the blowoff phenomenon of the Hall-effect propulsion system. From a 600-W class Hall thruster, we observe the oscillatory behavior of the anode current with a frequency of 34–38 kHz, which sometimes leads to plasma blowoff. We employ an output-only system identification framework that uses the noise-induced dynamics at this frequency, extracting linear and nonlinear coefficients of the low-order system model. The computed coefficients suggest that the plasma blowoff is characterized by large linear and small nonlinear parameters of the stochastic Van der Pol equation. From the obtained results, we conclude that this framework can be exploited either to identify a reliable operating condition with a low possibility of plasma blowoff or to diagnose the blowoff susceptibility of the thruster. This research constitutes the first application of stochastic system identification to the Hall-effect thruster, opening new possibilities for avoiding unwanted oscillations and blowoff phenomena in electric propulsion systems.