David Doherty, 26, of Salford, suffered lacerations to his lower back when he was attacked at the Appleby Horse Fair in Cumbria in June.
Cumbria Constabulary said a large group of people filmed the incident in the Market Field area of the fair on their mobile phones and cameras, and issued an appeal for witnesses to come forward last month.
Mr Doherty was taken to Cumberland Infirmary in Carlisle following the attack at about 12.35pm on June 5 but was released later the same day.
His father, Paddy, has been thrown into the media spotlight following his appearance in the hit Channel 4 documentary series and is currently a contestant in the latest series of Celebrity Big Brother.
Tommy Morrison, 29, of Toll Bar, Doncaster, South Yorkshire, and Luke Morrison, 26, of Barnsley, South Yorkshire, had been accused of Section 18 grievous bodily harm but the case against them was dropped at Carlisle Crown Court on Wednesday.
A court spokeswoman said: “This case is now discontinued due to lack of independent evidence.”