How to crop DWG files to sheet size when exporting?

If I am exporting a SW drawing file as a PDF, it automatically crops out anything outside of the sheet view, but when I try to export a DWG, it includes these things and shows them off screen. How can I get a DWG that is just cropped to the sheet size like it does with PDFs? I went through the options and tried both "Export active sheet only" and "Export all drawing sheets to paper space," neither worked. In the sample below I show what the SW drawing file, the exported PDF, and the exported DWG files look like. 

SolidworksEdrawings