The electromagnetic spectrum registered via satellite remote sensing methods became a popular data source that can enrich traditional methods of vegetation monitoring. The European Space Agency Sentinel-2 mission, thanks to its spatial (10–20 m) and spectral resolution (12 spectral bands registered in visible-, near-, and mid-infrared spectrum) and primarily its short revisit time (5 days), helps to provide reliable and accurate material for the identification of mountain vegetation. Using the support vector machines (SVM) algorithm and reference data (botanical map of non-forest vegetation, field survey data, and high spatial resolution images) it was possible to classify eight vegetation types of Giant Mountains: bogs and fens, deciduous shrub vegetation, forests, grasslands, heathlands, subalpine tall forbs, subalpine dwarf pine scrubs, and rock and scree vegetation. Additional variables such as principal component analysis (PCA) bands and selected vegetation indices were included in the best classified dataset. The results of the iterative classification, repeated 100 times, were assessed as approximately 80% median overall accuracy (OA) based on multi-temporal datasets composed of images acquired through the vegetation growing season (from late spring to early autumn 2018), better than using a single-date scene (70%–72% OA). Additional variables did not significantly improve the results, showing the importance of spectral and temporal information themselves. Our study confirms the possibility of fully available data for the identification of mountain vegetation for management purposes and protection within national parks.