Understanding how RFID tags work is key to understanding how the NFC Kill works. In a nutshell, RFID tags can be thought of as wirelessly powered memory cards. The memory card is connected to the antenna - which is powered up when the tag is place in range of a reader.
When powered up, the "memory card" can communicate with the reader - to transmit its data, update its data, or perform other functions.
Because the data is stored on the tiny "memory card", or chip, which is often embedded in plastic or epoxy - it is very difficult to physically destroy the chip.
Colloquial practice is to cut the card - this will break the antenna - but will not destroy the data on the chip. Fixing or replacing the antenna will allow the chip to function again.
This is the same as unplugging a USB-drive. Even though the drive is un-powered, the data is still present.
As such, to permanently disable an RFID tag - the chip itself must be destroyed in a very specific manner.
The RFID chip runs at a very specific power level - which is managed by the reader. Not enough, and the chip can't power up - too much, and the chip will fail.
The NFCKill works by detecting and connecting with a RFID tag, and increasing the power until the chip fails. This physically destroys the chip and data - resulting in secure and permanent data removal.