Mirador does this, but it isn't very easy to extract for this pared-down purpose. With the right configuration, Mirador can become a cropping tool. It can also export the regions as OA/IIIF annotations.
I have been meaning to extract this functionality for some time, or otherwise create a callback in Mirador that would allow people to use it easily for this purpose.
For now, however, I think what would make the most sense as a start is to use the
osd-canvas-selector module under the IIIF Github organisation. This is the module that is used in Mirador for selecting regions of the canvas for annotation creation. It will allow you to extract regions in IIIF canvas coordinates from an openseadragon canvas in a very specific way (it will not force you to make an annotation, and simply returns the coordinates). Download it from github
here.
It is not as fully featured or easy to deploy (from a meta-project standpoint. It is simple to use.) as something like jCrop is for static images, and not documented very much (the example is a pretty complete starting point, however), but I would welcome any contribution to improve it along those lines into something like jCrop. File an issue if you need any help with it, and I or others in the community will do their best to address it and improve the tool in the ways the community needs. I haven't worked on it as a standalone component for some time, so any feedback on updates it may need would be very welcome.
-Drew