Cambiophagous insects, fires and windthrow cause significant forest disturbances, generating ecological changes and economical losses. The bark beetle (Ips typographus L.), inhabiting coniferous forests and eliminating weakened trees, plays a key role in posing a threat to tree stands, which are dominated by Norway spruce (Picea abies) and covers a large part of mountain areas, as well as the lowlands of Northern, Central and Eastern Europe. Due to the dynamics of the phenomena taking place, the EU recommends constant monitoring of forests in terms of large-area disturbances and factors affecting tree stands’ susceptibility to destruction. The right tools for this are multispectral satellite images, which regularly and free of charge provide up-to-date information on changes in the environment. The aim of this study was to develop a method of identifying disturbances of spruce stands, including the identification of bark beetle outbreaks. Sentinel 2 images from 2015–2018 were used for this purpose; the reference data were high-resolution aerial images, satellite WorldView 2, as well as field verification data. Support Vector Machines (SVM) distinguished six classes: deciduous forests, coniferous forests, grasslands, rocks, snags (dieback of standing trees) and cuts/windthrow. Remote sensing vegetation indices, Multivariate Alteration Detection (MAD), Multivariate Alteration Detection/Maximum Autocorrelation Factor (MAD/MAF), iteratively re-weighted Multivariate Alteration Detection (iMAD) and trained SVM signatures from another year, stacked band rasters allowed us to identify: (1) no changes; (2) dieback of standing trees; (3) logging or falling down of trees. The overall accuracy of the SVM classification oscillated between 97–99%; it was observed that in 2015–2018, as a result of the windthrow and bark beetle outbreaks and the consequences of those natural disturbances (e.g., sanitary cuts), approximately 62.5 km2 of coniferous stands (29%) died in the studied area of the Tatra Mountains.