How to prevent domain mirroring?
The good news is, Google should be able to recognize that you published the content first, meaning their copy is of less value. Be sure that you have some way to verify when your changes are published, such as pinging Google automatically when pages are updated, or marking last-updated timestamps on all of your pages, which can be automated in most CMSs. By having the earlier "last modified" date on your pages, Google and other bots can recognize that you are the one who published first and deserves the credit for the content.
You should also file a DMCA takedown request since they are violating copyright law.