Polygonati Rhizoma (PR), for which rapid geographical origin identification is crucial to ensure its efficacy and product authenticity, is a traditional Chinese medicine with multiple pharmacological effects such as hypoglycemic and anti-tumor effects. This study presents a rapid identification method of sliced PR geographical origin based on auto-focus laser-induced breakdown spectroscopy (LIBS) combined with interpretable machine learning. The spectral data of sliced PR samples from 8 producing areas were obtained by using the self-built auto-focus LIBS system without further sample processing. Various data preprocessing methods, feature variable selection methods, and classification algorithms were evaluated. The results showed that the combination of wavelet transform (WT), Model-Free (MF) algorithm, and area normalization (AN) outperformed each method used individually. Among the feature selection methods, iteratively retaining informative variables (IRIV), variable iterative space shrinkage approach (VISSA), and the successive projection algorithm (SPA), the fewest feature variables were selected by SPA. However, by combining with Linear discriminant analysis (LDA), K-nearest neighbors (KNN), Multilayer perceptron (MLP), and Support vector machine (SVM), a good prediction accuracy of 95.00% was still achieved by SPA-SVM. Furthermore, according to the importance analysis by the SHapley Additive exPlanations (SHAP) algorithm, Ca was the most essential element to distinguish sliced PR samples from different geographical origins, followed by other elements in the order of Fe, Ti, Sr, C, Mn, Mg, Li, Ba, K, H, Si, and Na. This study provides a simple, rapid, and reliable analytical approach for PR authentication, which has broader applications in medicinal material and food product verification.