Non-removable MDM profiles cannot officially removed without doing a full system wipe. This is a problem when you restore a system from Time Machine after you enrolled it into the MDM, as the MDM will break, leaving you unable to re-enroll the machine.
Here's how to remove a non-removable MDM profile Boot the Mac into Recovery Mode (hold down command+R during startup). Go to the Utilities menu and open Terminal and type: csrutil disable. This will disable SIP (System Integrity Protection). Reboot into the OS. Open the integrated terminal and type:
cd /var/db/ConfigurationProfiles
rm -rf *
mkdir Settings
touch Settings/.profilesAreInstalled
Reboot. Boot the Mac into Recovery Mode (hold down command+R during startup). Go to the Utilities menu and open Terminal and type: csrutil enable. This will re-enable SIP. Reboot into the OS. The profile will be now removed and you will be able to re-enroll the Mac to your MDM.