3 axis accelerometer for detection of cutting a fence
how could one detect, whether someone has cut the fence or not, using
  the accelerometer or any other sensor or electronic device.


If you threaded a "sense" wire that snaked left to right and from top to bottom and made that wire look like part of the fence, it's likely that someone cutting the fence will also cut the sense wire and this can be detected by a circuit quite easily.

The general idea is embodied in this type of product but it's quite easy to make your own: -