What is this paper/foil in between drywall and concrete block? Can I cut it and repair it?
The foil is either part of the insulation panels I think I see there or it's a separate product, but the intention is the same. It reflects radiant heat and stifles moisture movement. 

You can remove it in small areas without substantially affecting the insulation envelope of your home, but you should attempt to re-seal the area using appropriate materials. Duct tape isn't a good long-term product. I'd use housewrap tape, which has a more durable adhesive and film, or at least a good packaging tape.