In your virtual aliases map (e.g. /etc/postfix/virtual_alias_maps), add the following line:

john.doe@example.com devnull

In /etc/aliases, add the following line:

devnull:  /dev/null


This defines a mailbox named devnull and stores its contents in /dev/null.

Don't forget to update the alias caches and restart Postfix:

sudo postmap /etc/postfix/virtual_alias_maps
sudo newaliases
sudo service postfix restart