Hi Aaron,
May I first advise NOT to do a SQL delete. Creating a Blog Entry also creates items in other tables and doing a SQL delete will cause them to become out of sync.
Unfortunately there isn't a button that will delete them all for you but using Server Administration scripts we can accomplish the same.
1. First go to Control Panel > Communities, and click on the community of the blog entries you'd like to delete.
2. Write down the its ID.
3. Now Go to the Control Panel > Portal Administration > Script
4. Copy and paste the below code and where ##### is the ID of the site you'd like to rid of Blog entries.
1Packages.com.liferay.portlet.blogs.service.BlogsEntryLocalServiceUtil.deleteEntries(#####);
5. Execute.
That should be it.
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