Police confirmed the body of a cat was found in Goring at 9.30am on Wednesday (28 February).
The owner has been identified, police said.
The incident has been passed on to the Metropolitan Police, who are investigating a series of cat deaths in Operation Takahe.
A spokesman said: “Sussex Police is aware of the work of Op Takahe and where there is an indication that there might be a link with an incident in the county, we will refer it to colleagues at Metropolitan Police, who liaise with the South Norwood Animal Rescue Liberty charity (SNARL).”
Police ask anyone with information about the incident to report online at https://sussex.police.uk/appealresponse or call 101 quoting serial 267 of 28/02.
The Worthing Cat Welfare Trust, in Orchard Avenue, is warning cat owners to keep their cats in at night.
A spokesman said: “It has been brought to our attention that a much-loved cat has been found murdered and mutilated in the Goring area.
“We send our sincere condolences to his family.
“We would ask cat owners in and around Worthing to keep vigilant and please keep your cats in at night.
“How someone could do that to a defenceless cat just beggars belief, this person needs help, please report them to the police and let’s stop this before another cat dies, and another family has to grieve.”