The woman said her husband witnessed the first attack, which happened about 10pm on October 5. Two dogs had each grabbed one of Zac's legs and fled.
"My husband and our son gave chase but the dogs fled down a driveway on nearby Somerset Grove," she said.
"It was horrendous."
The dogs returned to the property twice, taking away Little Fluffy on the third occasion.
"When I saw one of the dogs on our property again and it had Little Fluffy in its mouth, I just screamed blue murder," the woman said.
She and her neighbour tracked the dogs back to a property in Somerset Grove.
The woman said she confronted the dogs' owner and demanded their cats' remains back but felt she was treated with total disdain and left the property in tears.
"It's been a bit of a nightmare and we're still trying to process what has happened. We've had to spend about $1000 to secure our property with gates to keep the dogs out.
"We absolutely fear because we have three other cats these dangerous dogs will come back. They need to be caught, next time it could be a child that is mauled."
She said one of the dogs was a big tan-coloured pitbull terrier, and the other was blackish-brown of an undetermined breed.
Her neighbour said he chased the dogs after hearing his neighbour's screams but did not witness the attack or see the cat in either of the dogs' mouths.
However, a young man who saw the dogs fleeing and also chased them had confirmed one of the dogs had Little Fluffy, but the dogs fled down a long driveway, he said
"I could see a number of dogs at the property so I wasn't prepared to go down there, to confront their owners. But my concern is these dogs could attack a little kid next time."
Devastated pet owner Peggy, who lives in nearby Oxford St, said about two weeks ago she found her cat Ging dead on her driveway after it had been savaged by a dog.
"I'm sure it was a tan-coloured mongrel which had tried to squeeze under my gate to get my cats before. I thought little Ging was just sleeping but he was stone dead and I found a large piece of his skin on the driveway. I just screamed and screamed," she said.
"I have had Ging for four years and he was such a lovely-natured beautiful intelligent cat. I miss him so much, and can't sleep, and I cry just talking about what happened. It's made my anxiety problems even worse," a tearful Peggy said.
Tauranga City Council's animal services team leader, Brent Lincoln, said the council was investigating complaints of dogs attacking four cats and possibly a dog in the area.
Lincoln said a search warrant was executed at an address in the area but the dogs at the property did not match the description of the alleged attack dogs, and inquiries were continuing.
Anyone who sees roaming dogs should immediately call the council, he said.