If it is acting fine, and swimming along, i would say it was a clean cut and it may heal, given the right circumstances.
Cooler water and salt. And eventually antibiotic though i do not use it. And extra clean water.
Chances are it won't make it. But you should decide now whether you want it to fight that battle, and do your best to keep her, if she survives or spare her that and kill it.
I, in your position, would keep her and gige her a tighting chance.