The household pet was found with an arrow through its neck by a farmer in Portaferry, who believes the animal was thrown from the window of a passing car.
The man, who asked to remain anonymous, said those responsible should be brought before the courts.
He told UTV: "It's a terrible act for somebody to have the guts to put an arrow through somebody's cat and throw it over the hedge into a field.
"I have children of my own who have pets and I know how they would feel if it was one of their cats or dogs lying with an arrow through its neck."
He added: "Obviously the owners of the cat are probably out looking for it.
"They would be better off not seeing what has happened to it and hopefully they will know, through this, what has happened to their pet."
SDLP Ards councillor Joe Boyle visited the scene of the attack after he heard about what had happened.
Really it’s just brutality towards a family pet.
Cllr Joe Boyle
He said: "It's horrific to see a cat killed with a crossbow.
"It's difficult to get into the mindset of those that did this - they might think it's a hobby or a pastime."
He continued: "It's very distressing, especially because this is someone's pet that has disappeared and the owners are probably waiting at home to see if it will ever return."
Bel Livingstone, from the Cats Protection, said incidents such as this were rare but that the brutality of this particular attack was shocking.
She said: "As the UK's leading feline charity we are horrified at this act of cruelty - we are heartbroken.
"We would strongly advise anyone who has information on this to contact the local PSNI and their welfare officer.
"We need to stop this sort of thing happening again.
"I haven't seen this in such a long time, it beggars belief why anyone would want to inflict that kind of pain or suffering on any animal."