Hayley Sulley, 30, and Della Woods, 29, both of Liverpool were charged under the Dangerous Dogs Act, after retired hospital porter Clifford Clarke died in May 2013.
Clarke was "eaten alive" by the dog, which had not been fed for 45 hours, when he opened his back door.
Judge Mark Brown said Clarke's death was "entirely avoidable" and he was "literally eaten alive" as he died in "truly horrific circumstances".
Sulley and Woods admitted allowing their dog to enter a non-public place and subsequently cause injury.
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Neighbours reported the animal, a Presa Canario and bull mastiff cross-breed, was foaming at the mouth and one said it appeared to be eating Clarke's arm.
The court heard the "wild" and "out of control" dog sank its teeth into Clarke's arm and dragged him around his garden; chewing his one arm off at the elbow and mauling the other.
Clarke died from multiple injuries and blood loss.
Judge Brown said Sulley and Woods were fortunate not to have been charged with manslaughter.
The women also pleaded guilty to three counts of causing unnecessary suffering to a dog at an earlier hearing and have been banned from keeping dogs.
Both bull mastiff and Presa Canario dogs are large powerful breeds but they are not banned in the UK.
In May, tougher penalties were introduced for dog owners in England and Wales who allow their pets to attack people.
The two women admitted the charges before the changes came into force and the new rules cannot be applied retrospectively.