I have been digging through some of the closed bug reports and found this report I wrote on a bug with 1.8.11:
This is the bug I was referring to in my reply to you earlier, it was a while ago but I was sure I remembered an issue relating to tags applied to Displays and the inability to delete Display Groups. This issue was a bug with Xibo which was fixed for the 1.8.12 release of CMS.
This is why I have asked you to upgrade your CMS, because issues that have been discovered are resolved in future revisions. This issue sounds a lot like what you are describing and you are using the same version as this bug was discovered on.
Regarding resolving issues without upgrading your CMS, this is not always possible, as some issues require a fix which can only be applied to a future release of Xibo. If you find that after you have upgraded your CMS you are still unable to delete the Display Groups, you will need to use the Report Fault option in your CMS as I suggested, so we can find out what is causing the issue. Without Logs, I do not have any information about the error.