The num in numskull and numb are both from nomme - the past participle of nim "to take" (as in German nehmen). The earliest meaning of nomme was "deprived of physical sensation", ie "taken". Nim fell out of use around the 15th century. It's from Proto-Indo-European *nem- "to assign, allot" (not this *nem-).
The OED says the semantic development from "allot" to "take" is difficult to account for, but to me it seems like auto-antonymy, similar to how bad is used to mean "good".
The Greek derivative νέμω "to allot" became νέμεσις "distribution of what is due, retribution", and Nemesis, the goddess of retribution.
There's a similar connection between distributing things and deities with *bhag-.