Google saves those messages off the phone in its servers, so I'm not sure you can delete all messages from the account without deleting the account from the phone. Deleting the account from the phone will NOT delete the Google account, but merely the account on the phone itself.
NOTE: If this is the account you logged into the phone with and sync to Play with for apps and settings, removing this account would be BAD! Consider merely archiving those messages instead if you wish to keep the phone. To proceed:
Go to Settings --> Accounts --> Google and select the account you wish to remove from the phone. In the menu (3 dots, upper right) select "remove account".
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