There are calls for tougher penalties for animal cruelty offences after a spate of attacks on dogs in Tasmania.

The RSPCA is investigating the death of a six-month-old puppy found in Launceston yesterday with a brick tied around its neck.

The organisation posted a photo online calling for information, which was shared about 3,000 times.

Three weeks ago, a Rocherlea woman reported that an intruder had chopped the leg off her dog in her backyard.

The dog, which already had a leg amputated, had to be put down.

The maximum penalty for aggravated cruelty carries a $26,000 fine and an 18-month jail term.

But the RSPCA says it the penalty has never been handed out.

President Paul Swiatkowski says the incidents are abhorrent and penalties need to be tougher.

"Even over a maximum penalty, most of the penalties that have been handed down are a slap on the wrist," he said.

Launceston alderman Rob Soward says there was also a social media photo post yesterday of a man people claimed had been forcing his dogs to sit on a jack jumper ant nest in a Riverside park.

"There's just some horrific stuff going on and again we want the State Government to really put some meat into the penalties," he said.

"We think that at the moment they're just slap-on-the wrist penalties."

Alderman Soward says the the public is outraged about the latest incidents and there has been a huge response on to a petition he posted on social media.

It received over 1,000 signatures in 15 hours.

"To me that says very loud and clear that there is no argument that the penalty shouldn't be tougher."

"We call on the State Government, the Opposition and the Greens to come together and listen to the voice of the people."

Tasmania's Attorney-General Brian Wightman says he is disgusted by the incidents and new legislation is already being drafted.

"One of those will increase the penalty form 18 months to five years imprisonment," he said.

The Opposition Leader, Will Hodgman, says a Liberal Government would consider tougher penalties.

"Certainly it is an abhorrent thing to see people mistreating animals and we take very seriously the need for government to play a pro-active role in reducing the incidence of these sorts of activities.

"We will always look at ways to ensure the laws are sufficiently tight," said Mr Hodgman.

Social media users have also responded to the incidents.

A Facebook page set up for the dog which had its leg cut off has garnered nearly 4,000 supporters.

A Facebook post about the ant nest incident has been shared almost 1,500 times.

The RSPCA is urging anyone with information about the attacks to come forward.