If you would like to disable cron job mail alert through cPanel then simply click on Cron Jobs page and don’t set any email address and clink on Update Email. You would see something like below:

cPanel says

You can have cron send an email everytime it runs a command. If you do not want an email to be sent for an individual cron job you can redirect the command’s output to /dev/null like this: mycommand >/dev/null 2>&1

But it did not work for me though.

This may be helpful if you have SSH access or root access.