The stability of deeply excavated slopes for road foundations can be assessed using the limit equilibrium method. In this approach, the stability coefficient, commonly referred to as the factor of safety (FS), is calculated as the ratio of the total moment (or total force) resisting slope failure to the total moment (or force) that contributes to that failure. In the design of excavated slopes, especially when digging deep (H ≥ 12 m), FS is often determined in the natural and saturated state which is then used as a basis for slope design as well as using appropriate anti-slip reinforcement measures. Although it is a critical coefficient, the reliability of FS depends on many different factors, especially the input parameters of soil and rock and the analyst’s skills. In this study, 210 cross-sections of deeply excavated slopes for road foundations on a newly designed route (Tuyen Quang–Ha Giang expressway, Vietnam) were analyzed and calculated. Out of these, the FS values of these cross-sections determined by the Bishop method in the case of the saturated slopes were used as output variables. Other variables such as slope coefficient, slope height, number of excavation mechanisms, weight of soils, thickness of soil layers, internal friction angle of soil layers, and cohesion of soil layers were used as input variables in the prediction models. In building the FS prediction models, four machine learning (ML) techniques were built and trained, namely Extra Trees Regressor (ET), Support vector machine (SVM), AdaBoost (AB), and a new hybrid model, namely SVM-SMA which is a combination of SVM and Slime Mold optimization Algorithm (SMA). The performance of the models was evaluated by the determination coefficient (R2), mean absolute error (MAE), and root mean square error (RMSE). The results show that all the models have good results in predicting FS, but the SVM-SMA model is the most accurate (R2 = 0.947, RMSE = 0.078, and MAE = 0.068). Therefore, it can be concluded that the SVM-SMA model is a promising tool for the rapid and accurate prediction of the factor of safety (FS) for deeply excavated slopes in road foundations, even in saturated soil conditions.