My question, too. Seems like it would be trying to work around a life-threatening wound, only now with a foreign object in it.
I would think the surgical strategy would involve gaining control of blood flow to the involved vessels at a location remote from the wound and then addressing the vascular damage at the wound site. (It could still be danged difficult to remove, but the problem of bleeding out would be controlled.)
I think the bottom line is to buy time to get where better care can be obtained.
I am assuming when they run into an injury treated like this or the old school way is that they have to go upstream and stop the flow, then clean all of this out, then do a massive repair. There is going to be a lot of extra cutting. One thing about hemostatic bandages is that they always tell you to pin or tape the package to the victim in a very conspicuous place so the medical professionals know what type it is and how to clean it out.