Cut it off! It will cause more damage and pain if she catches it on something and tears it off. If you don't have styptic power available, have some cornstarch or even flour to help stop any bleeding. Good old fashioned sustained pressure will also work.
I have more than once cut my cavies' nails too short and caused them to bleed. There is something called vet glue that is used on cats when they are declawed. It will also work, but it literally dries in seconds so you have to be precise when applying it. The vet glue is a type of tissue adhesive that is great for small cuts on humans as well, as it is the same chemical that for humans is called Dermabond which is often used for skin closures when sutures are not desirable.
A tissue adhesive such as this is often used by Vets after a cavy neuter.It's ultimately safer so that the boy doesn't pick at his stitches.
Both Dermabond and Vet Glue have similar chemical components as are present in Krazy Glue. I have even used that when nothing else is available.
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