Can gravitational field be cut off?

Not really. Gravity determined by the mass of the objects near you. And there is nothing that will intercept these gravitational forces, preventing them from acting on your body.

Having said that, one can counteract gravity in a sense. The simplest way is seen in astronaut training, when to simulate an environment with no gravity acting on the person, they will fly a plane for a short time in an unpowered parabolic arc. Since the plane and the individuals inside the plane are both accelerating towards the ground at an acceleration of 1G, no gravity is felt. The person inside the plane feels as if they are weightless. In fact, they are in the presence of a gravitational field, but temporarily they do not notice the effects of that field.

http://express.howstuffworks.com/falling-up2.htm

The same is true for an astronaut in orbit around the Earth. Are they weightless? They still have mass, and therefore inertia. But because a person in orbit is constantly falling towards the earth, they feel as if they are essentially weightless. Again, gravity is still there and acting on your body, even when you may not explicitly feel the effects of the gravitational field.

Likewise, gravity can be simulated in space, by rotating the craft that you fly in. This rotation confers a centripetal force to your body, which feels just like the acceleration due to gravity. It is not gravity, but your body does not know the difference.

You notice the effects of a gravitational field when you are standing (or sitting) on the surface of a planet (or moon, whatever.) Think of it as a "potential well". You feel gravity because your legs oppose the attraction of gravity on your body. It is this opposition to gravity that you notice. Or, suppose you try to lift a large rock from the ground, or a paper weight from your desk. It is only by your attempting to resist gravity that you feel it. Were you to fall in free fall in a vacuum with that paper weight in your hands, it would be falling with you, so it would feel weightless. Remember, it still has mass, therefore inertia, but no weight.

So can you cut off a gravitational field? No. At best you can (possibly only temporarily) not see the effects of a gravitational field. Unless of course you write science fiction. There anything is possible.

If you mean the earth gravitional field so Of course NO!! because the gravitional force resulted from rotating the earth around it self with a very high speed which make a gravitional field as it rotates around the sun .

The gravitional field stops cut off in one case if the earth stop rotation and in that case it will fall in the sun due to the sun's incredible gravity;D.