I am trying to do a temporal analysis on vegetation quality so I downloaded a MODIS .hds raster from earthexplorer. When I opened the file into ArcMap 10.2.2, it came as a group of 11 rasters. I stuck on clipping those rasters by my shapefile and combining them into one. (tried, clip raster by shapefile, composite bands...)
Clipping *.hdf files in ArcGIS may not be a good idea as ArcGIS doesn't deal with HDF files very well. I would recommend you convert the HDF files into some other formats (eg, tif) first and then clip them in ArcGIS.