SD card shows up as Internal in Disk Utility
You cannot back it up if the partition information is damaged. You first need to repair the damage. Sounds like it is the root/boot disk, which means you don't want to try using it. 

Yes you can boot your damaged Mac into Target disk mode by pressing the T key right after powering it on. Then plug it into another Mac. The damaged disk will appear as a drive on the good Mac. Run diskutil to repair your damaged disk.