There are a few ways of doing this and all basically involve using the reverse proxy or "ProxyPass" feature of Apache to accomplish it.
1.) Create a normal vhost and simply symlink the root directory of the site you want to mirror.
Eg. originalsite.com and newsite.com
You would symlink like this:
ln -s /vhosts/originalsite.com/httpdocs vhosts/originalsite.com/........
This is a great way to use your ftp server space, for example on your web hosting account (althoughI believe many hosts don't allow storage like this), but if you have a VPS/Dedicated Server etc.., this would be perfect. Imagine how easy it is to work with an ftp account that you can just mount as a normal partition or directory in Linux, it would be great for backups etc..
curlftpfs - mount a ftp host as a local directory