Is there a way to perform a 'reverse' of the clip function in ArcMap?
I am not exactly sure how to explain this so here is a diagram:
Use the Erase (Analysis) Tool:
Since Erase (as @Jens linked) only is available with an Advanced license, you can download ET Geowizards. It can be installed as an Arcmap toolbox.
Although you have to pay for the full suite, there's a free part of the program and the Erase function is included there (Overlay group).
Another free option if you don't have an Advanced license for ArcGIS is the Xtools Pro extension suite. Like ET Geowizards, some of the tools are only available if you buy a license but most of them are free forever, the Erase tool is one of the free ones.
Another option here would be to perform a
union and then delete the inner feature. After the union,
select features from the initial layer and use the
delete feature tool to remove the selected polygons.
How many polygons are you needing to 'reverse clip'?
IF it's just one or two, turn on your editing, select ALL the features that come into contact with this 'erase' polygon, then trace the erase polygon with the cut polygons editing tool. It'll slice up all your selected polygons. Unselect everything, then reselect the ones to delete, and just delete them. Silly workaround, but effective if you only have a few areas to 'reverse clip'.
I have found this method to work:
Your "clip" feature layer will still be in tact, so go ahead and turn this layer off. This should perform a reverse clip.
Here is the code to do ERASE without advanced license.
Check out the select by location option. You can select all points falling within a feature layer. After these have been selected, go to the attributes and switch the selection.