In my case I had done a trial backup/restore onto an older laptop and the disk was fairly small, thus backups filled up the disks and kept sending me messages.
First su to the zimbra user
su - zimbra
The it's probably a good idea to see what the current schedule is and save it in case you want to restore it later.
zmschedulebackup -q
f 0 1 * * 6 -a all --mail-report
i 0 1 * * 0-5 --mail-report
d 1m 0 0 * * * --mail-report
Lastly use the -F (Flush) flag to delete the current schedule.
zmschedulebackup -F
Congratulations! You now have 0 scheduled backups..I hope that's what you really wanted.
