Can you please tell me as much as you can from the point of getting the info? I'm not going to do this right now because it's late for me and I can do this in the day when it's easier to concentrate for me. Thank you.
[doublepost=1544157724][/doublepost]Is this what you were asking for?
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that drive is formatted APFS. Do a get info on the Time Machine volume. It should be formatted HFS+ or Mac OS Extended (Journaled). If it is formatted anything else, that is why Time Machine doesn't work. If it is properly formatted, then the problem is something else. If Time Machine worked prior to installing the beta, then remove the beta (you _do_ have a _full_, _working_, _tested_ backup from _before_ you installed the beta, right?) and see if the problem goes away.
Alternatively, Apple has released 10.14.2. Go to the App Store and download the _full_ updater, which should be around 5 GB. Update to the release version and see if Time Machine works now. If it doesn't you have a problem, but it's not with the beta.
May I suggest using something like SuperDuper! or Carbon Copy Cloner to make backups? May I also suggest that you avoid installing betas, of anything, until you work out what the problem is with your system?