David Ellam, 52, suffered multiple injuries after trying to fight off the Staffordshire-Labrador crossbreed while walking his own dog near his home.
His death came just a week after the animal had been returned to its owner by police, following concerns that it was a dangerous breed.
Officers said later that a control order had been issued in October 2012, putting in place strict conditions for its management. The order remains in place.
Neighbours in Riddings Road, Huddersfield, said yesterday that it had attacked at least four other people, and had acted with such ferocity that council workers had refused to cut the grass nearby.
Lionel Brown, 55, said he was among those to have been attacked by the animal, whose owner called it Ali.
He said: “About two or three years ago it came for me when I was taking out the bins. It nipped me on the face and around the mouth and on my leg.
“I told the police because I was worried it would go for someone else, but they didn’t take it away.”
Another neighbour added: “The dog has gone for at least four people before the man who died. He is the fifth.
“It got to the stage where I would never venture out if the dog was in the garden.”
Mr Ellam’s family described his death as “such a shock for the family”.
A relative, Sarah Clark, said: “Everybody loved him. He was such a kind and gentle person and it has cost him his life.”
Detective Chief Inspector Mark Swift, of West Yorkshire Police, said: “Mr Ellam died following multiple injuries sustained during the incident on Monday morning and our inquiries are continuing into the circumstances.
“I would appeal to anyone who was in the area who may have not yet spoken to police, who has any relevant information, to come forward.”
Mr Swift said: “We appreciate there will be understandable concern following this tragic event. There continues to be an increased visible policing presence in the area to offer reassurance to the community, and I would urge anyone who has any concerns to speak to officers.”
He said the suspect dog remains in kennels while the investigation continues.
The 29-year-old owner of the dog was arrested in connection with the incident and later released on police bail.