Do TV aerial cables carry electricity?
Then, is it safe to cut through a TV aerial cable?
Usually a TV antenna cable (called coaxial cable or just coax) carries only low voltages that are not dangerous to humans. For this reason it's a good idea to use insulated wire cutters when cutting a coax cable that is connected in any way to equipment.
Beside this, what is the difference between air and cable on a TV?
The obvious difference between cable and OTA TV is channel-density. Cable TV is comprised of a few thousand channels, while OTA TV only broadcasts (at max) 69 channels for each locality.
There is no way you should ever get a shock by touching the shield (outer conductor) on a pice of coax. That's the whole point of the grounding provisions of the NEC: to see to it no one gets shocked.