In situ mineralogical and chemical analyses of rock samples using a space-prototype laser ablation ionization mass spectrometer along with unsupervised machine learning are powerful tools for the study of surface samples on planetary bodies. This potential is demonstrated through the examination of a thin section of a terrestrial rock sample in the laboratory. Autonomous isolation of mineral phases within the acquired mass spectrometric data is achieved with two dimensionality reduction techniques: uniform manifold approximation and projection (UMAP) and density-preserving variation of UMAP (densMAP), and the density-based clustering algorithm Hierarchical Density-Based Spatial Clustering of Applications with Noise (HDBSCAN). Both densMAP and UMAP yield comparable outcomes, successfully isolating the major mineral phases fluorapatite, calcite, and forsterite in the studied rock sample. Notably, densMAP reveals additional insights into the composition of the sample through outlier detection, uncovering signals from the trace minerals pyrite, rutile, baddeleyite, and uranothorianite. Through a grid search, the stability of the methods over a broad model parameter space is confirmed, revealing a correlation between the level of data preprocessing and the resulting clustering quality. Consequently, these methods represent effective strategies for data reduction, highlighting their potential application on board spacecraft to obtain direct and quantitative information on the chemical composition and mineralogy of planetary surfaces and to optimize mission returns through the unsupervised selection of valuable data.