When you have two (or more) sites' databases in a single MySQL database you need to use the RegEx Database Filters feature. As noted in the end of the documentation page I linked, you can create a new regex filter with the content
This tells Akeeba Backup to skip over any table which does not belong to the joomla installation being currently backed up.
Merely as an aside: For site performance and security reasons it is very strongly recommended that you create one MySQL database per site. While Akeeba Backup can work around multiple sites' database tables occupying space in the same MySQL database this is far from being your only problem. Versions of Joomla released in the last decade (3.4 and later) use the InnoDB table format for most tables. This format shares a single data file across all tables. Having the InnoDB tables of two sites share the same database increases the chance of a read/write lock when accessing database data which can have a performance impact on your site, especially if both sites have a fair amount of traffic. Moreover, by sharing the same MySQL database you have a security issue. If one site gets compromised (hacked) then BOTH sites are hacked since each site can access the other site's tables, including the tables which handle users and extension configuration. This is merely for your information, so you can make informed decisions about the performance and security of your sites.
Nicholas K. Dionysopoulos
Lead Developer and Director
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