Delete overlapping faces between two objects Is it possible to select parts of one layer in the outliner and then delete it from another layer in the outliner?

I have two objects that overlap and I want to delete the parts that overlap.

I want to be able to select the top and delete the vertices from the body in the shape of the top so that the object underneath the top is deleted but the top remains.
I know how to do it face by face but I was hoping there was a shortcut like the selection tool in Photoshop that works between layers.
You can try using the mask modifier. If you want another work around select in the mesh the limits that you want to cut and hit the V key to separate after that hit the L key to select the mesh island then delete the unwanted piece. You may also separate the selection as an object with the p key.