You could import the backup set to local backups (if not already present in local backups), then descend into the DUMP_D directory defined in psa.conf and get the database dump from there. You can import that dump file into any database you like.
Example: Assume that your local backups are stored in the default /var/lib/psa/dumps. You'd then descend into /var/lib/psa/dumps/clients/<user name>/domains/<domain name>/databases. There you will find a dump file for each database, e.g.
drwxr-xr-x 2 root root 4096 Jan 25 23:35 johndoe_wp_0meuk_1
Although this file is not ending on .sql, it's a normal SQL dump text file that can be imported into any database.