With that said, we do provide the ability to hook your own scripts and commands into the backup process itself, for instance backing up MySQL you'd just put in the mysqldump command (with relevant DB and user/pass info) into the hook script uncleverly titlted 'run-before-backup.sh' in the config directory.
I personally don't have any experience with Redmine. Application-specific backups are outside the scope of our initial launch, but as we get more user feedback we'll be able to build plugins that integrate with specific applications. In the mean time, I'd both: 1) pester the developers to provide a simple backup solution for Redmine, and 2) look into either putting it on a VM that you can snapshot, or use something like ZFS snapshots and send/receive it to a remote location.