If you're receiving too much spam despite forwarding errors to assp-spam@yourdomain.com, you can increase your antispam sensitivity from normal to high, higher, or highest in the ASSP section of your cPanel. If spam still passes through at these settings, check the email headers, as the sender is likely whitelisted.
To remove a sender from the whitelist, send an email to assp-notwhite@yourdomain.com with the sender's email address in the body of the message.