Target Disk Mode - How to delete files while in Target Disk Mode?

If the drive of the Mac in Target Disk Mode is using the APFS file system and there is no free space available, then you will be unable to delete any files due to how the APFS file system works.

Maybe you can get lucky and see if there are any APFS snapshots on that drive which can be deleted which may free up the space needed. Here are a couple of articles about APFS snapshots, but the instructions will need to be modified slightly since you will be trying to delete APFS snapshots from an external drive (the examples assume you are accessing the boot drive).

View APFS snapshots in Disk Utility on Mac - Apple Support

https://eshop.macsales.com/blog/56681-working-with-macos-snapshots/

https://derflounder.wordpress.com/2018/04/07/reclaiming-drive-space-by-thinning-apple-file-system-snapshot-backups/

FYI, macOS always needs at least 20GB of free storage space at all times for the normal operation of macOS. Even that 20GB can quickly disappear during normal used due to temp & cache files utilized by the various apps.

You should always have frequent and regular backups of your computer and all external media (including the cloud) which contains important & unique data. You never know when it may be necessary to erase the whole drive to fix an issue (it may be the case here).

If the machine is in Target Disk Mode deleting files should be as simple as dragging them to the Trash and emptying the Trash. You can also right click the files and move them to the Trash from the window that pops up.

That program is considered malware and should be uninstalled. It also may be the source of the problem you are experiencing. I would strongly recommend uninstalling CMM and reformatting the drive. Then restart the Mac in Safe Mode and then start over with your project. Failing that, please give AppleCare a call.

Can you tell me why you have a drive called "CleanMyMac 3" ??

I'm sorry I simply have not run into this before. BTW, I am in Folsom.