To improve the accuracy of water inrush and mud outburst disaster prediction during tunnel construction through karst caves, a method of first forecasting the unfavorable geological conditions of karst caves and subsequently predicting water inrush and mud outburst geological disasters was proposed in this paper. First, a karst cave advanced prediction model based on the polynomial naive Bayes algorithm was established to predict the scale grade of karst caves. Secondly, taking the scale prediction results of karst caves as the input condition for water inrush and mud outburst, a support vector machine (SVM) grade prediction model for karst cave water inrush and mud outburst based on the genetic algorithm (GA) was established. The random seed was regarded as an optimizable hyperparameter, and the overall training effect of machine learning models could be improved by adjusting the random seed during data partitioning; the prediction imputation methods, namely the K-nearest neighbor algorithm and SMOTE algorithm, were adopted to generate synthetic samples to fill in missing sample values and solve the problem of sample imbalance. By comparing the GA-SVM model with three models (SVM, GS-SVM, and IPOS-SVM), the results indicate that the overall prediction accuracy of the GA-SVM model is the highest. Model testing demonstrates that the accuracy of the comprehensive advanced prediction model for karst caves is 81.25%, and the accuracy of the grade prediction model for water inrush and mud outburst is 91.67%. Applications in multiple tunnels indicate good effects, and the research results provide a new method for the prediction of water inrush and mud outburst in tunnel karst caves.