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A mountainous road network with special geological and meteorological characteristics is extremely vulnerable to nonrecurring accidents, such as traffic crashes and geohazard breakdowns. Geohazard accidents significantly impact the operation of the road network. Timely and accurate prediction of how long geohazard accidents will last is of significant importance to regional traffic safety management and control schemes. However, none of the existing studies focus on the topic of predicting geohazard accident duration on regional large-scale road networks. To fill this gap, this paper proposes an approach integrated with the Kaplan–Meier (K-M) model and random survival forest (RSF) model for geohazard accident duration prediction based on text data collected from mountainous road networks in Yunnan, China. The results indicate that geohazard accidents in road networks have a strong aggregation in tectonically active, steep mountainous, and fragmented areas. Especially the time of the rainy season, and the morning peak, brings high incident occurrences. In addition, accident type, secondary accidents, impounded vehicles or personnel, morning rush hour, closed roads, and accident management level significantly affect the duration of road geohazards. The RSF model was 0.756 and 0.867 in terms of the C-index and the average area under the curve, respectively, outperforming the traditional hazard model (Cox proportional hazards regression) and other survival machine learning models (survival support vector machine). Without censored data, the mean absolute error and mean squared error of the RSF model were 11.32 and 346.99, respectively, which were higher than the machine learning models (random forest and extreme gradient boosting model).