A 'GIS' is just a mathematical tool, it takes any sort of data given to it for analysis and visualization. Is your question about where to find existing GIS data on types of minerals, or maybe how various different sensors are used to identify various minerals? That can range from core samples from boreholes, seismographic returns from underground, to field surveys on the surface, to multi-spectral and hyper-spectral signals observed from space.
If you have a satellite image of the area of interest where you know exactly what type of rocks there are you can teach the system what each type of rocks looks like. This is called supervised classification. Then use the satellite imagery from unknown rocks and ask the system to classify the rocks. The detailed procedures are outlined in ESRI web site
GIS alone cannot help you detect rock types. two technologies that complement each other well in this regard are GIS and remote sensing. the detection is done by use of remote sensing, in form of either aerial photographs or satellite images. Appropriate analysis of the aerial photos or remote sensing image data will help you to distinguish areas underlain by different rock type, based on the different spectral signatures, textures or structures they display at the surface. The photo or image analysis alone is not sufficient to make conclusive identification of the rock type. Conclusive identification is done by confirming the actual rock types represented by each of the different categories identified in the images or photographs, through groundtruthing. The role of GIS now may be reduced to only enabling a more presentable cartographic outlay and visualization of the final geological map.
Remote Sensing is where you can do a lithological discrimination using different tools.
Mineral indices can guide in making alteration maps, Band ratios in rgb can dicriminate rock contacts and visualizing structures, Imagery classification can generate a geological map based on training samples , and more and more
But
GIS is how you can manage and visualize vector data