You can perform a backup using a command like the one below, which will ensure it is done with lower priority on the disk. This way, the sites may not become unresponsive, or you can use Percona XtraBackup for backup, which will not affect the operation of the sites. I will try both and update you.
ionice -c2 -n7 mysqldump -u your_username -p your_database_name > backup.sql
