The hydrogeochemistry of deep groundwater needs to be characterized for geological CO2 storage or radioactive waste disposal. However, various origins and their interactions and complex hydrogeological conditions make it difficult to assess. Moreover, it is challenging to interpret a large national dataset of hydrochemical variables due to wide composition ranges. This study aimed to define the representative geochemical facies of deep groundwater (average well depth of 624 ± 262 m) obtained from spa areas over South Korea by applying both linear (principal component analysis; PCA) and non-linear (self-organizing map; SOM) dimensionality reduction methods to a large dataset (n = 355) with 16 hydrochemical variables. The SOM results combined with hierarchical cluster analysis showed that deep thermal groundwater in South Korea is classified into five major geochemical groups (G1 to G5) with four mixing groups (M1 to M4). G1 to G5 represent high-TDS saline (7% of the samples), acidic CO2-rich (4%), high-pH alkaline (14%), sulfate-rich (9%), and dilute freshwater (11%), respectively. More than half of the samples (56%) belonged to the four mixing groups. In particular, the SOM reduced the number of samples (n = 355) to 104 neurons, visualizing the cluster structure of samples and the relationship among hydrochemical variables in a 2D array of neurons, which made it possible to distinguish the facies (G4 and G5 and M1 to M4) that could not be defined by PCA due to the extremely distinct geochemistry of G1 and G2. Based on the compositional changes of neurons between the geochemical (G1 to G5) and mixing (M1 to M4) groups, major reaction pathways were identified for each geochemical group. The hydrochemistry of each group mainly evolves through distinct water–rock interactions but is modified by varying degrees of mixing with dilute shallow groundwater during ascent. This study provides a state-of-the-art method to interpret a large and complex hydrogeochemical dataset; the SOM is expected to be a useful alternative to PCA. Besides, the results of this study can be useful to select a site suitable for geological CO2 storage or radioactive waste disposal.