BUP is a nice git-based backup tool that is both free and easy to use and saves space by differential backups.
You can also use bup to backup a MySQL database using mysqldump directly instead of first dumping to a .sql file and then backing up the file.
This is possible by piping the mysqldump output directly into bup split:
mysqldump [...]| bup -d $BUP_DIR split -n mysqldump.sql
By using -n mysqldump.sql you are telling bup that the file created by the dumping should be named mysqldump.sql in the backup.
Full example:
export BUP_DIR=/var/lib/bup/mysql.bup
export MARIADB_ROOT_PASSWORD=piahaen9ehilei0Ieneirohthue4Iu
bup -d $BUP_DIR init
mysqldump -uroot -p${MARIADB_ROOT_PASSWORD} --all-databases | bup -d $BUP_DIR split -n mysqldump.sql