According to the Justice for Max GiveALittle page, Max was killed on his own property.
"Max's family came home on Friday the 23rd of June to find him dead on their front lawn, they rushed him to the vet where it was discovered Max had been shot in the chest.
"Max was on his own fully fenced, fully contained property."
The page has been set up to raise funds to help find Max's killer and has put up a reward for any information.
Locals have hit out on Facebook vowing to find the person responsible.
"Karma is going to find you," one person wrote.
"The sick freaks doing this must be found, they are dangerous," another said.
The SPCA has said it is unusual to have a string of cases of animal cruelty and is appealing to anyone with information to come forward.
It is not known if the cases are connected.
Locals fear further attacks will take place.
"Hence why i put cameras up around my place after i had paint marks put up my fence and same as someone else who had dogs in the area," one person wrote.
Another local has called for community action, saying: "Invercargill people - talk to your neighbours, if you are away during the day, make sure someone is watching after your pets. What is happening is disgusting and has to be stopped."