Good idea; I've often wanted this too. Another option would be to just put a checkbox before the relationship option, though the current Mantis interface isn't laid out in the best way for this. Maybe a "not related to" menu selection is the easiest after all.

I tracked this down and it is a simple fix. There is already a function in relationship_api.php I think that was intended for this. It is called relationship_list_box_for_cloned_bug().

So the two places you need to change this are:
bug_report_advanced_page.php line 443
bug_report_page.php line 331

Calling this function puts these items in the dropbox:
No Relationship
Related To
Parent Of
Child Of

The things it would remove would be:
Duplicate of
Has Duplicate

Which I think are pointless anyway when you are cloning an issue, but it appears other people are requesting this feature (0005113) so it wouldnt bother me to leave it in.