Its best to deal with this sort of thing on the Gmail web portal.
I'm aware of one person who deleted his Archived Mail folder on his Mac only to find he deleted all mail from all mailboxes! I can't vouch for exactly what he did as it had already happened when I got the panic phone call but I can vouch for the fact that while we were able to retrieve everything, jumping through hoops doesn't do justice to the hassle!
I'm not sure you can stop them all being stored there - that's what Gmail does but you should be able to delete emails from within it using the Gmail webmail interface.
I use Apple Mail to get my emails from gmail, it puts a duplicate copy of each email in the Archived Mail box. I go through this box on occasions and delete them but the originals are still in the in box or other folders I have put them in