Menu: Edit -> Cut
Accelerator: Ctrl + X
Toolbar: 
Drag and drop: see below
Cut removes the selected logfilter or subfilter from the filterset pane (including its subfilters) and moves it to the clipboard. All references to the cut logfilter will be destroyed. If the filter is assigned to the logmessage pane it will be released (unassigned).
If the cut logfilter contains references to other logfilters these logfilters will be copied to the clipboard as empty filters.
Using drag and drop for cut and paste:
For cut and paste you can also drag a filter / subfilter and drop it over another filter / subfilter while pressing the Shift key.