If you have access to the Spatial Analyst Extension, one option is to use Map Algebra:
A quick tour of using Map Algebra—ArcGIS Help | ArcGIS for Desktop
One workflow would use SetNull to Null out all the values of cells that match your "Erase" raster. Note that you may have to do a processing step first to set up your Erase raster to give it distinct values so the SetNull can work as desired. This can be done with Con or Reclassify.
Set Null—Help | ArcGIS for Desktop
Con—Help | ArcGIS for Desktop
Reclassify—Help | ArcGIS for Desktop
Chris Donohue, GISP