Eight other officers suffered cuts and bruises in the fracas and six people were arrested.
PC Paul Rogers's screams were heard through his personal radio as he called for assistance in Ramshead Drive, Seacroft, Leeds.
A colleague dragged him free into their patrol car. Insp Neil Fawcett said: 'We take a very serious view of an incident where a large ferocious dog is used as a dangerous weapon against officers.
'It's sad to have to kill the dog but there was no option.'
PC Rogers, 27, was said to be comfortable last night in St James's Hospital, Leeds, after an operation on his leg injuries.