A copied Shopify store, product descriptions, photography, even the layout, is fundamentally a copyright question, and it's handled through the same DMCA process as any other hosted content, not a Shopify-specific system.
Before anything else, two things are worth checking. First, whether the copy is exact or just similar. Product descriptions that use common industry phrasing will look alike across unrelated stores. That's not infringement. Product photography and written copy that's been directly lifted, sometimes still carrying your own file names or watermark, is a much clearer case.
Second, whether the store is actually selling a competing or counterfeit product, or just using similar language to describe a genuinely different product. Those are different problems with different solutions: one is a copyright issue about your content, the other may be a trademark or counterfeit issue about your brand.
Once you've confirmed genuine copying, the practical next step is the same as any other hosted-content case: identify who actually hosts the infringing store, often but not always Shopify itself, and prepare a notice identifying your original content and the specific location it's been copied to. Screenshots with visible timestamps, and side-by-side comparisons where possible, are the evidence that moves fastest.
If your store content has been copied:
We confirm what's actually been copied, identify the hosting party, and prepare the notice, so nothing gets filed against the wrong target.