I don't believe that your body will completely get rid of the virus, it can become dormant and it may or may not come back at a later date. I could be wrong but that is my understanding.
I understand (and believe) what Andiesq says. Your body will always maintain a history of having had the virus. It is possible that the virus could be reactivated later in life and cause more problems down the road.
So no. There is no way (that I know of) to rid the body of HPV.
That doesn't mean it will always be active and will always cause problems.