You can open phpmyadmin (or something similar), and export the database.
Then install a new MyBB copy, complete the install, then drop all tables in database and import your copy.
Remember that some plugins include their own tables of the database, so they're completely useless and you can choose to drop them or keep them, either works.
However, if you want to completely clone the website (as using the method above won't include the theme, you'll need to export that and reinstall), you can always just make a complete copy... Then all you need to do is disable all plugins, and you can use the backup of the forum without any active plugins in it.