The RSPCA says four terrified kittens were tied up in a carrier bag and thrown over a six foot wall in Barnsley.
The cats were found by a woman who was walking her dogs in the cemetery on Cemetery Road last Wednesday.
She took the kittens home, alerted the RSPCA, and they were rushed to a nearby vets.
It was feared one of the cats wouldn't survive as he was very poorly and weak but he is now said to be doing well.
Another of the kittens has a leg injury but is expected to make a full recovery.
Jackie Siddall, from the RSPCA Barnsley and District branch, said: “The poor kittens were obviously trembling and terrified when we collected them and two were in poor health. It must have been a dreadful ordeal for them.
“I am delighted to say they are now doing well and our dedicated fosterer is hand rearing them to build up their strength as they only weighed 300 grammes - and is busy with night feeds too.
“They are all gorgeous and when they are old enough we will find them loving forever homes.”
The RSPCA is now appealing for information to find the person who left the kittens.
SPCA chief inspector for South Yorkshire, Lyndsey Harris said: “These poor defenceless kittens were discarded like rubbish we believe due to their injuries they had been thrown over a six feet-high wall.
“It’s always heartbreaking when I deal with abandonments. We are seeing increasing numbers of cats and kittens coming into our care. Perhaps in this case the owner decided the kittens would be too much work for them so instead of being responsible and contacting a rehoming charity for help they callously discarded them and left them to die.”