We've customized to this requirement before, but unfortunately, it's been a while and I can't recall the precise mechanism we took. If my vague memory is correct, we had users access the "crop-as-new-image" function via a small custom workflow (accessed via a custom menu button) that leveraged the same UI as the out-of-the-box crop, but since we'd forked that OTB code, we could take a different result.
I would say that crops in the AEM tool are almost never the right way for users to handle cropping. Most creatives are more comfortable in Photoshop for something like this and would rather access the asset via Asset Link or Desktop app to make a quick adjustment--and they could easily save the adjustment as a new image. That would avoid the need for customization altogether and keep creative users making modifications in the Creative Cloud tool with which they're more comfortable.
Lastly, if you were going to customize to provide a technical solution, I'd look strongly at Smart Cropping as your starting point if Dynamic Media is owned (rather than the older AEM Edit function). You could customize the Smart Crop adjustment screen to add a "Save Smart Crop as New Image" function and the back-end code to submit the Smart Crop as a new image (and probably create a Source relationship) shouldn't be too hard.
Hope this helps,
Beau
