Police were called in after abuse was hurled at Councillor Malcolm Cunning.
Thugs trashed the Labour councillor's car by scrawling the slogan "Yes" across the bonnet.
But since the attack, earlier this week, online abuse has escalated into postings of harassing and vile threats.
One independence supporter -who had the 'Yes' slogan on their account - even posted part of Mr Cunning's home address on Twitter.
Mr Cunning, who represents the Linn ward on the South Side, said: "The whole thing is creepy, especially when they are posting part of my address.
"These messages clearly threaten further damage to my car.
"I've reported the matter to the police, who are investigating."
Mr Cunning said decent Yes supporters were horrified and had offered their support.
However, he slammed the "vandalism and abuse" which has become associated with the discussion of Scottish independence.
Earlier this week, we told how Mr Cunning's car was vandalised by yobs. He feared damage had been scratched into the bodywork and reported the attack, yards from his Cathcart home, to the police.
The incident comes after Harry Potter author JK Rowling was abused online for giving £1million to Better Together.
Scotland's top law officer warned both cybernats and unionists to stop making abusive remarks - or risk jail.
Frank Mulholland, the Lord Advocate, said there was "a line which should not be crossed".
The Crown Office is expected to issue guidelines for social media, making clear when online actions are a crime.