Welcome to iPhoneForums, jumper82!
In Settings - Mail, Contacts, Calendars, go to Account and select the Gmail account. Tap the email address and choose Advanced next.
Take a look at "Move Discarded Messages into:" and make sure Archive Mailbox is not selected there. It should be "Deleted Mailbox".
Next place to look at, is in "Mailbox Behaviours", above "Move discarded...". Go to "Deleted Mailbox". What is checkmarked there? (On my iPhone, or On the Server). Usually, it's "On the server" - Bin. This will remove the emails from your iPhone.
It's also possible that you have to look at your settings in the Gmail account online. In that case, login to the account through a browser.
Another option to solve problems with email accounts is to remove them completely and set them up again. If nothing else works, try it.