Christopher Nicol, 27, was stabbed at a flat in Maple Road, Greenock, Inverclyde, at around 9pm on Thursday September 26.
The attack happened in front of his two young children, aged five and six, who are now being looked after by their mother.
Mr Nicol's mother Karen has now made an emotional appeal to find "the man responsible" who "ruined the lives of all our family".
She said: "I am devastated by the tragic death of my much-loved son Christopher. Our lives have been changed forever.
"He was a brilliant dad to his two young children, whom he worshipped and would have done anything for.
"The man responsible has taken one life and ruined the lives of all our family.
"Please, please if you have any information that will help officers, then call the police or Crimestoppers, as soon as possible."
Officers returned to the scene a week after the incident, stopping seven vehicles and speaking to six passers-by in the hope of jogging their memories and discovering new lines of inquiry.
The suspect is described as white, aged 20-30 and has a local accent.
He is about 5ft 9in and of slim build with an unkempt, reddish, brown beard and moustache, with bad teeth and some visibly missing.
At the time he was wearing a black beanie hat with a logo, possibly Timberland, a black top and black jeans or trousers.
Police plea for more information
Detective Chief Inspector Martin Fergus said: "Throughout the last fortnight, extensive inquiries have been ongoing to trace the man responsible for Christopher's violent murder.
"Although I am encouraged by the public response to our previous appeal, I am in no doubt that there are people in the area who may have seen or heard something, and we still need to speak to them urgently.
"Although people may think the detail they hold is insignificant, it could indeed be that smallest piece of information that moves our investigation that crucial step forward.
"If there is anyone you know who is acting differently from usual, or who may have become withdrawn, then please get in touch.
"If anyone has overheard anything or has suspicions about someone, then please let us know.
"This man was violently attacked in front of his two young children and I do believe that somebody local knows who is responsible.
"Therefore, I am again urging anyone who holds any detail on Christopher's death to do the right thing and come forward."
Anyone with information is asked to contact police via 101 quoting incident number 3888 of September 26, or anonymously through Crimestoppers on 0800 555 111.