I was able to create a private category. I was able to assign a group to that category. But, it’s also allowing all admins to view the category. Is there a way to only allow the users from a particular group to access the category, excluding the admin group? Only admins who are in that particular group may view the category.
Is this possible?
You can’t exclude admins, no. They are all seeing, afaik. 
Yep, any viewing restriction you could place on admins would be artificial as they could just download a backup and peek in there. You have to trust somebody.
Here’s the scenario that I’m trying to address.
I have a forum consisting of a small community where everyone knows each other. In this forum, there’s a group made specifically for women where they can share their thoughts without any men viewing the content. There’s a female admin who is managing that section. However, we don’t want the male admins to be able to see the category. I understand that admins can pull the backup and view the topics in that category, but we don’t plan to. Is this possible?
Only if you make the uh… people who should not view that content non-admins.
Are there particular functions your admins are doing that require that level of access? It may be worth revisiting who can do what if you have this as a content-security issue.
You could write a tiny plugin that monkey-patches the User class and overwrites the secure_category_ids method…
However, in the interest of fairness, everyone on your forum should be aware that all admins can at any time view all content; the only thing such a change can do is to reduce temptation to give in to curiosity.
No, admins can not be restricted, they can download the database if they wish and look at the tables.