A group of respected party activists, with a high-profile presence on social media, has begun policing offensive comments on blogs and social networking site Twitter.
In a separate move, the pro-independence Yes Scotland campaign has highlighted warnings to supporters not to make personal attacks or engage in abuse.
The problem is not limited to the nationalist side of the referendum debate, with the SNP complaining of Unionist "unitrolls" spreading online abuse.
The latest spat followed BBC reports on the Scottish Government's decision to accept a more neutrally-worded referendum question, which attracted more than 1300 comments on the corporation's website.
SNP activist Calum Cashley stepped in to silence a cybernat called SNPDunblane who prompted a furious online backlash after suggesting the BBC should not have allowed comments on the issue from outside Scotland. The user later deleted his comments and the account was closed down.
Mr Cashley, a former SNP candidate who works as policy director for MEP Alyn Smith, said: "The abuse comes from both sides, it comes from Unionists as well. But it is taking away from political debate. It is damaging our cause and it is damaging the Unionist cause.
"If you think about the people not on either side who are looking for information, they will be thinking what the hell is going on? If you saw a fight in the street you would not go near it and it's the same online."
He added: "We have started to challenge them and ask them what they think gives them the right to be so bloody rude.
"It is not a party thing. The problem is they are not party members. The party does not know who they are."
The latest Twitter row came as the Yes Scotland campaign emailed supporters reminding them of online guidance published last year.
It states: "Someone who does not agree with us should be treated with respect. Politics is all about different viewpoints. Never make personal attacks on any individual or engage in general abuse of opponents. The key to victory is positive persuasion. Our case is a strong one and there is no need to become involved in personal attacks."
Labour MSP Richard Simpson said: "This sort of online abuse of anyone who disagrees with the SNP is unacceptable. I hope the SNP gets control of its supporters who hurl abuse and denigrate anyone who disagrees with them."
Yes Scotland insisted it had not highlighted its guidelines in response to the latest Twitter row. A campaign spokesman said: "We would hope anyone who uses social media – from whichever side of the fence –uses it courteously, sensitively and responsibly."
A spokesman for the SNP said: "The SNP's social media guidelines are robust, as shown by the fact that this Twitter account was taken down."