You can delete the selected text in an edit component without cutting it to the clipboard. To do so, call the ClearSelection method. For example, if you have a Delete item on the Edit menu, your code could look like this:

procedure TEditForm.Delete(Sender: TObject);
begin
  RichEdit1.ClearSelection;
end;

void __fastcall TMainForm::EditDeleteClick(TObject *Sender)
{
  RichEdit1->ClearSelection();
}