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/
2.) A flexible way and the best way if you want the mirror/different site to have a different IP address but still serve the same content.
This would be in your vhost.conf
ProxyPass / http://yourmainsite.com/
ProxyPassReverse / http://yourmainsite.com/
Alternative Way If You Want To Proxy The Same Domain through a different IP (eg. for SEO geolocation purposes you could host all content on a single server and then put proxies in front of it)
ProxyPass / http://ip.ip.ip.ip/
ProxyPassReverse / http://ip.ip.ip.ip/
*Make sure you keep the "/" at the end of yourmainsite.com or it will not work properly.
The above is a preferable for me because it will keep working even if the backend server config or IP changes.
When doing this with live, public sites that are indexed in search engines you could get penalized or just plain confuse people so there are issues to handle.
First of all if you force all requests to go to a certain domain or on SSL, you will have to consider how to handle it by updating your .htaccess
Also if you don't want to get penalized for duplicate content, you will need to add some code to your site to determine if it is being accessed by the main host name, if not then you should dynamically insert a nofollow and noindex into your <head> section.
<meta name="robots" content="noindex, nofollow" />
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