Basemaps are tiled image services - they are a picture (just for backdrop) they are not elevation data.
I think what you want are ArcGIS Online imagery layers, these are raster data you can work with directly. There is a nice imagery layer in the ArcGIS Online Portal called Terrain that allows you to download elevation, slope, etc.
If you create a local raster you must save it locally (for example as a .tif) or as a file geodatabase raster.