Can not access or mount external encrypted APFS disk

You tried to "repair" the entire "disk3" which I'm not sure you can do. I think you need to specify a partition/volume such as "disk3s2".

Try using the command line to unlock the Filevault without mounting the volume. If the volume is unlocked, then try using the command line to mount the volume read-only. macOS can get into a weird state after attempting to mount a volume as evidenced by the "disk4s1" listing here. I would reboot the Mac, then try to manually unlock and mount the drive read-only. Assuming the external drive is still "disk3" after the reboot the commands should be:

diskutil  ap  unlockVolume  -nomount  disk3s2

diskutil  mount  readOnly  disk3s2

Note: Or the mount device may need to be "disk4s1" (double-check the information from diskutil ap list to see if "disk4s1" or another drive identifier is linked to "disk3s2" like it is shown in your screenshot).

When I've encountered APFS Filevaulted drives that could not be mounted I've never been able to manually mount them read-only as there is always file system corruption preventing the unlocked APFS volume from mounting read-only.

There is a possibility your external drive is failing. You can attempt to check the health of the external drive by running DriveDx. You will need to install a special USB driver so that DriveDX can communicate properly with the USB drive. Even with this special driver DriveDx may not be able to access the health information on the external drive because some USB controllers used by external drives don't allow the necessary communication. Post the DriveDx report for the external drive here using the "Additional Text" icon which looks like a piece of paper. If DriveDx reports any failures, then stop using the drive immediately or you risk the failure getting worse.

As @steve626 mentions there are no third party utilities to repair the APFS file system. After that you will need to contact a professional data recovery service such as Drive Savers or Ontrack. Both vendors provide free estimates and both are recommended by Apple.

You should have frequent & regular backups of any external media that contains important and unique information as well as your boot drive.

Try using DriveDx before you unlock the Filevault as unlocking the drive and attempting to mount the drive may be interfering.

You can try unlocking the Filevault as I described earlier to try using a data recovery app such as Data Rescue.

The best way to perform a bit for bit clone of a drive is by using the command line utility GNU ddrescue which is similar to "dd", but is able to handle errors thrown up by a failing drive plus it can resume an interrupted clone and is able to show you the progress. However, the command line utilities are dangerous to use as it is very easy to mix up the source & destination locations and destroy what you are trying to save. You will need an equal or larger size drive if you perform a bit for bit clone (not all 1TB drives have the exact same storage area -- probably not a big deal in most cases).

As long as the external drive is not throwing physical errors, then you can use macOS and GNU ddrescue by installing GNU ddrescue by using Homebrew. If the drive is throwing errors, then performing the clone using a Linux boot disk is best since macOS cannot handle the errors. You need to use the GNU ddrescue logging/mapping file in order to resume an interrupted clone. If a clone is interrupted you must always re-verify the source & destination drive identifiers before resuming the clone and make any appropriate adjustments.

If the physical drive is causing the problem in mounting the file system, then most times it is possible to mount the clone with good hardware, although if the file system is corrupt and Disk Utility is unable to repair it, then you are stuck since there are no third party utilities for repairing the APFS file system.

A bit for bit can easily copy an encrypted drive without issues. The encryption key is stored on the drive and is copied along with everything else. As long as the encryption key is not damaged it should be possible to unlock the Filevaulted clone. I've recovered data from hundreds of failing encrypted macOS hard drives using this technique (I've actually used a Linux system to perform the clone).

Have you tried First Aid through Disk Utility itself? Presumably yes and presumably did not work (as diskutil Repair failed, but I don't understand the "Invalid request" error message.) Have you tried First Aid at all levels of the drive?

With Filevault encrypted drives, the encryption is so strong that usually the only recovery possible is from a backup. Do you have one? Disconnecting the USB wire while still mounted could have left the drive in an unrecoverable state, the partition map may have been damaged. Normally repairable ... but often not with APFS or Filevault ...

Is this a mechanical drive? Is it USB powered? If yes to both questions, the situation may be grave because if it was actually accessing a platter when power was pulled the disk itself could be physically damaged beyond repair.

Even if unencrypted, there are very few APFS utilities that can repair APFS file system errors (Disk Utility has limited repair capabilities, tools like Disk Warrior are not yet APFS enabled.)

Returning to the time you entered the encryption password unsuccessfully ... Apple sets up an alternate way to unlock the drive when you first configure the drive and encrypt it. Did you have a recovery key, or did you use your iCloud account/password for that? Can you revert to that alternate way to unlock the drive?

ignitemymac wrote:

What might be a repair tool that can handle APFS drives?

I have looked into this in the past year and it seems that there has not been enough information released yet on Apple's APFS implementation for third party vendors to create utilities to repair the file systems in APFS analogous to what had been done for the earlier HFS+ file systems. I'm referring to the multiple often very powerful utilities such as Disk Warrior, TechTool Pro, Data Rescue, Disk Drill, etc. Some of these (Disk Warrior) state that at this time they cannot be used to repair damaged APFS drives, others claim to be able to do it (TechTool Pro). If you research this a bit online, you will see that even when manufacturers claim they can repair APFS damaged drives, in practice what they can do is reported by some to be a lot less than what used to be possible with HFS+. Most of these products offer a free trial download so you can sort of try it out with your situation before buying the product. I have TechTool Pro but have never tried it on an APFS drive as the opportunity has never arisen for me. APFS drives are supposed to be more resilient, but mishaps like yours will still occur. I always rely on multiple backups (of different types) for protection. For a drive that won't mount or appears to be irretrievably damaged, Apple always recommends an erase/reformat with restore from backup. If you don't have such a backup, then perhaps your best bet is to explore some of these disk repair utilities, but for APFS, the options are limited.

Is this an SSD or HDD? For HDD, there are other options, albeit expensive, where companies will take apart the drive platters and retrieve the bits (ones and zeroes) from the physical surfaces, and in this way some files can be reconstructed. The cost can run into thousands of dollars, however, as this is laborious work done in a clean room. For SSDs, I think the chances of recovery are much lower, either with a disk repair tool or a clean room recovery.

One last Hail Mary type effort might include taking the drive out of its current enclosure and putting it into a new one. This is relatively low cost and it would address the possibility of some electrical or firmware damage to the enclosure (with the drive itself still healthy) caused by the mishap. In other words, enclosure failure, not drive failure.

CCC used to have an option for block copying of drives, but I think that was on HFS+ drives in an older version. Maybe check their web site to see if this option still exists or if it exists for APFS.

You might also investigate the unix command dd as that might make a bit for bit copy of a drive. (Watch out for different block sizes on the source and destination drives, however.) I am not an expert user of dd, however, so research it first with the available documentation (use Terminal).

Problem is, since the source volume is Filevault encrypted, I think a bit for bit copy will be unreadable hash as it must be unlocked/decrypted to make any sense. If the partition maps were damaged on the source, not sure how that damage can be overcome on a duplicate copy.