On Tumblr, you can make a secondary blog somewhat private by setting a password on it. See [How to Create a Secondary Blog on Tumblr] for details. Then in order to access the blog, a visitor would need to know the password. Of course, if they share the password with everybody, it wouldn't be very private anymore.
It's not possible password-protect your primary blog. You must create a secondary one.
If you have already created a secondary blog, you can add or remove a password to it in its Blog settings page. It's the same page you go to change its avatar. The password setting is all the way to the bottom.
It's not possible to allow only users whom you follow, i.e. your "mutuals" to access your blog, which is something you would be able to do in platforms like Instagram.
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