Two 4TB hard drives -- how can I create a RAID 1 with two 2TB partitions? I have been struggling with trying to get Disk Utility to allow me to divide a 4TB HD into two 2TB partitions, and then have a mirrored raid of that for redundancy.  Is this not possible?
It is not possible and even if it were it would be a very bad idea.
RAID 1 is to protect from hardware failure, and as described in the Apple document Create a disk set using Disk Utility on Mac mentioned by @user3439894 in comments, requires multiple disks (not partitions).


Mirrored (RAID 1) set: Protect your data against hardware failure with a mirrored RAID set. When you create a mirrored RAID set, your data is written to multiple disks so the information is stored redundantly.


Even if it were possible it would provide no protection against hardware failure (as both partitions are on the same disk) and in the case of a HDD would drastically reduce write performance as the disk arm would have to continuously jump back and forward between partitions.
While it may theoretically give some limited protection against bad blocks if you only have one disk you would be much better off making a a backup to another partition (which would protect you from accidental file deletion).  Backup to another to another disk would protect you from disk failure and file loss while RAID 1 is only designed to protect from hardware failure.