Hello,
DXF is data translation from one format to another. Hence, exports the whole content of the file.
Comparing to the PDF export, the PDF is a print, hence catches the printable area only while exporting as PDF.
There is hence no way to exclude drawing view to be considred for DXF/DWG export.
Better approach is "Erase View" like said by @MartinHanak
A mapkey with PAUSE can be programmed to make things somehow fast.
A side point is that "put a drawing view in a layer in order to hide the layer" is not possible and there is no setting to do that .. Items in drawing view (surf, edg, curve, ...) can be added to layer but not the view .. Just try create a new layer and go to filter in bottom right corner and will not find "drawing view". All accessible for selection is the solid geom that implies ALL solid geom in drawing sheet will be hidden once you hide the layer.