I have a DEM and I have a shapefile showing polygons that represent mounded features. I want to create a DEM which has 'holes' in the data where the mounds occur. This is because I wish to regrid it and then subtract this hypothetical bathymetric map without mounds from the original in order to work out the mound heights.
Also if you can think of an easier way to calculate mound heights please let me know.
Have you tried creating a polygon shapefile with the reverse of what you already have? Assuming you don't have ArcEditor or one of the higher end licenses, you could create a polygon the same size as your DEM area (i.e., so as to preserve the extent), and then union this with the mounds polygons. From the unioned feature class delete your mound areas, leaving a swiss-cheese like area (i.e, area without mounds). Then use this feature class to clip your raster. Would that work?