Theres a few scripts for sale on black hat forums and marketplaces that automate this DNS/Iframe copying of sites. (It's not really copying as your site is served from your server into an Iframe on the culprits site). The script automates everything including setting up the web server on a cloud VPS e.g.: Digital Ocean, Linode etc. I'm not going to link to them for obvious reasons but the cost is about $20 - $50 depending on which script it is.
The best way to prevent this is detailed here.
.htaccess - How to Block Iframe call - Stack Overflow