The incident happened on Newhaven Place in the Newhaven area of the city shortly after midnight on Wednesday, April 24.
The 20-year-old owner was approached while walking his Shih Tzu Westie cross in Newhaven Place.
He was approached by an unknown man who began to assault him. A second man exited a grey vehicle (similar to a Vauxhall Corsa) and also assaulted the victim.
The two men then walked the victim around the corner to Glenarm Place where he was confronted by a third male suspect who had a weapon.
This third suspect then stole the victim’s mobile phone and his beloved dog.
The three men then assaulted the victim again before all three left in an unknown direction in the grey car.
The victim sustained minor injuries and did not require medical attention. Police were called and officers are now investigating.
The first suspect is described as a white man between the ages of 30-40-years-old. He is around 5ft 9” to 6ft in height with a stocky build. He was wearing a black jacket with white logo on the left sleeve, black trousers, black shoes, and a black beanie hat. He spoke with a Glaswegian accent.
The second suspect is described as male, around 5ft 8” to 5ft 10” with a slim build. He was wearing a black long sleeved top, black trousers with a white strip and white logo on the left leg and black balaclava (or hat and scarf covering his face).
The third suspect is described as a male between the ages of 20-30-years-old. He has a medium build and short dark hair. He was wearing a dark grey long sleeved top with black sides, black joggers and red trainers.
Detective Inspector Graham Grant of Edinburgh’s Criminal Investigation Department said: “This was an appalling attack on a young man, which has resulted being traumatised and losing his family’s dog.
“This level of violence is completely unacceptable in our communities and we are eager to trace the three men responsible for this attack as soon as possible.
“I would ask anyone who was in the Newhaven area just after midnight on Wednesday, April 24, and has any information that might help our enquiries, to get in touch with us at their earliest convenience.”
Those with information can contact Police Scotland on 101, quoting incident number 0087 of April 24, or anonymously via Crimestoppers on 0800 555 111.
The incident comes after a man jumped from a car and tried to snatch a dog in George Terrace in Loanhead on Monday.
A Police Scotland spokesperson said at the time: "A male was seen to exit a red car and reach over a garden fence before being challenged by a neighbour and leaving the area.