Time machine says backup drive is full. How do I purge things in my iMac so it can fit?

If you erase the TM drive for re-use, yes, you will lose the TM backups and all other contents.

Copying a TM backup is possible, but not something I’d generally recommend. It’s excruciatingly slow.

Set the old TM backup aside, until you’re sure you don’t need it.

Until your new TM has some depth.

Then re-use the old TM.

That 2 TB Time Machine drive is far too small for your needs.

That is big enough for cloning a backup, but not for Time Machine.

Not with that nearly 2 TB source device.

Time Machine tries to keep revisions as files change, and there’s just no room for keeping copies of changes here.

I’d go with a 4 TB Time Machine drive here minimally, and probably preferably larger.

Preferably 5 or 6 TB, for more backup depth.

Want to use that 2 TB drive for backups?

Get CCC or similar tool, or use Disk Utility from Recovery, and clone.

Downside? You have no depth if backup, with just one clone.

And you might have no backups, if the source drive fails part way through the clone.

I’d boot the Mac into Safe Mode too, and see if some of that purgeable can be freed.

Click on the blue-colored text in my previous reply (and in this reply) for more information; blue here indicates a hyperlink.

There are tools to check content, GrandPerspective and OmniDiskSweeper being useful.

I’d expect a 2 TB Time Machine target is too small for a 2 TB source device, unless you have a habit of running with (well) under a TB of content, and/or churn only with small files, and/or seldom churn files. 2x is what I’d consider minimal, and more when bigger files and/or higher rates of file churn are involved.

If you have multiple Macs, you can either use a Mac as a Time Machine server—a Mac with a lot of storage configured—or can install and use a network-attached storage (NAS) box such as the Synology DS220+ or another Time Machine capable option.

The nice thing about NAS storage for a laptop particularly is that the backups happen when the Mac is connected to the same Wi-Fi. You don’t have to remember to cable the storage, or be next to the storage to cable it,

You should replace the drive with one that is about 3 times the size of your boot drive. I have a 6TB drive for my boot drive and two external HDs that total 2.5 TB in capacity. This drive would also be a good choice for your 2 TB drive: OWC Mercury Elite Pro 6.0TB 7200 RPM Storage 

You can use your current drive to make a clone of your boot drive with Carbon Copy Cloner as a second backup.

You do not have to purge any files. Time Machine initially does a complete back up for you. It may take some time, but won't interfere with your use of the computer. Backups may be encrypted if you wish. Subsequent to the initial backup, all other backups are only those things which have been added or changed. When the backup disk becomes full, Time Machine begins overwriting the older files. Everything is done automatically according to a prearranged schedule. I think it's every hour. The drive you use to backup to should be three times as large as your hard drive. When someone has a smaller backup drive, as you do, for some reason it makes it difficult for the app to do it's job. That's why you are getting the message.I am sure that a larger backup drive will work just fine. I hope this is helpful.

Marty Roberts wrote:

I downloaded omni disk sweeper and it is running, but not sure I can tell what to delete.

You can delete your stuff, from your own home directory and its subdirectories.

You don’t want to and increasingly can’t delete macOS stuff.

You will want to reboot through Safe Mode to clear up temporary usage.

elp me understand how I can make a clone of the backup? Where would it go if everything is full?

Correct. You don’t have anywhere to do that cloned backup without clobbering your Time Machine backup. I was referring to what was and is possible as a use for that 2 TB disk, once it’s no longer a Time Machine backup target. Or what can be done, given the disk isn’t really big enough for Time Machine.

The CCC tool is one means to clone, and the Safe Mode boot stuff was linked in an earlier reply.

Booting macOS Recovery and running Disk Utility is a bit more involved. And you’ll still need somewhere to copy the backup.

I’m usually running Seagate 5 to 6 TB external hard disks for Macs that need simple backups and which is similar to what you’re seemingly doing here, and running NAS storage and RAID storage arrays for more serious storage and backup requirements. Which might be a bit above your requirements.