The case HAS USB3, but the Mini can't "see" it?
What FORMAT is the drive currently in?
Can Disk Utility see the drive "on the bus"?
Even if it won't "mount up" in the finder?
In that case, I'd copy the contents of the drive to another drive.
Then... I'd open Disk Utility and ERASE the drive, using "Mac OS extended with journaling enabled, GUID partition format".
Then... I'd restore the data to it.
If the Mac still won't recognize the drive after trying that...
... I'd try a different enclosure.