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/........