sh-3.2$ mutt -s "BIYG backup `date +%m-%d-%y`" -n -F /dev/null -a /home/xxx/backup/biyg_backup_`date +%y%m%d`.tgz xxx@gmail.com < /dev/null
sh-3.2$
Obviously, if you copied your line correctly, there is a missing backtick.
Backticks mean the same as old "eval", actually yours was intended to add the
result of a formatted date (but that's malformed as well) to the subject.
As an example, date "+%d.%m.%Y" gives the current date in day.month.year notification.
Your line most likely should look more like mutt -s "BIYG backup `date +"%y-%m-%d"`
5 4 * * sun rm -rf /home/xxx/backup/biyg*
5 3 * * * /home/xxx/bkup
5 6 * * sat mutt -s "BIYG backup `date +%m-%d-%y`" -n -F /dev/null -a /home/xxx/backup/biyg_backup_`date +%y%m%d`.tgz xxx@gmail.com < /dev/null
(D=$(/bin/date "+%m-%d-%y"); /usr/bin/mutt -s "BIYG backup $D" -n -F /dev/null -a "/home/xxx/backup/biyg_backup_$D.tgz")
The first two work, but the mutt one doesn't. Now if I copy-paste that mutt syntax, it'll work. But for some reason I'm not getting emails from that cron.