A much-loved family dog is dead after being stabbed in a Melbourne backyard with police chasing a scent for whoever attacked Vuk, the Maltese-cross-Jack Russell.

The 11-year-old canine was found suffering two stab wounds at his home on Fifth Avenue at Dandenong on Tuesday morning.

Owner Vera Novakovic reportedly saw a trail of blood to the back door before finding the dog covered in blood about 6am.

She tried to take Vuk to the vet, but realised one of her car tyres had been slashed.

Vuk had to be euthanased a couple of hours later.

"Only a sick person would do this. You are mentally disturbed -- get help," she told News Corp Australia.

Ms Novakovic's mother reportedly heard the dog barking about 4am but could not find the dog, who had been freed from his leash earlier after being frightened by fireworks.

While the stabbing and tyre slashing are believed to be linked, police said the family did not notice anything else suspicious overnight, and a motive is yet to be determined.

Detective Sergeant Nick Lamb told AAP the incident could have happened between 2 and 5am, and there had not been any complaints about the dog leading up to the incident.

"(He) was part of their family. It had been with them a long time," he said.

Police have not ruled out whether the dog was stabbed while trying to protect the home and released an image of Vuk in the hope witnesses or the offender will come forward.

poor baby