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The hunt "ran out of control" after a dog took hold of the terrified kitty, which was in a private garden.
The pooch was then reported to have "shook [the cat] like a rag doll", according to The Independent.
The hounds "ran ahead of the horses uncontrolled" while the riders were out exercising with them.
Hunt organisers, from High Peak Hunt, have since pledged to review their protocols in order to prevent another pet being murdered.
Speaking of the incident, the cat's owner, Rebecca Bingham, said her two year old cat Spider was sitting on a wall in her garden when the hounds sprinted in.
"Before she had chance to move, one jumped up on the wall," she said. "She then dodged and hid underneath the car, but it crawled under after her, brought her out, jaws clamped around her stomach, and shook her like a rag doll.
"But by the time we managed to get the dog to release her, she was the gasping for air, and within a minute she was passed away."
Describing her pet, Rebecca called Spider "a real beauty, and was still in my eyes a baby".
She added that the hounds had frequently tried to break into her garden in the past.
"We have had to remove them from our property more than once because of this," she said.
A local anti-hunt group has since appealed for locals to submit information to police and the RSPCA, should they be able to help.
Responding, a from the High Peak Hunt said the hounds are often exercised by professional hunt staff without any issues, but apologised unreservedly for the tragedy.
"The hunt has been in contact with the cat owner and apologised unreservedly for the distress this has caused," they said.
"Incidents of this nature involving hounds are incredibly rare due to the professionalism with which the hounds are handled in kennels and throughout their lives; however, the hunt has taken this matter very seriously and is reviewing their procedures to prevent any reoccurrence."
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