> when i use it (click  it), it ask always me to make
> an "update" of the website, so i will lost all the
> pages now deleted by the webmaster.
Exactly. Deleted pages will be removed from the mirror, by default, on a
update.
If you set the 'do not purge', they won't be deleted but won't be connected to
the mirror either.

If you already updated the mirror, the files have been deleted. They are gone.
You can only restore them from backups.