The move to keep The Scottish Republican Socialist Movement (SRSM) away from next weekend's rally came after opposition politicians used its involvement to embarrass Salmond.
The First Minister was criticised for agreeing to speak at the cross-party "rally for independence" in Edinburgh, for which the SRSM was officially described as a participating group.
The SRSM campaigns for an end to capitalism and the violent overthrow of the ruling class under the slogan "Revolution not Devolution!".
In a sign the gloves are now well and truly off in the independence debate, the pro-Union Better Together campaign circulated a detailed media briefing about the SRSM on Friday.
It accused Salmond of sharing a platform with "a group who regularly burn Union flags, attack the Queen, glorify terrorism and advocate a violent Scottish revolution."
It drew attention to the group's description of 1970s tartan terrorists as "political prisoners" and highlighted YouTube videos showing the SRSM's ritual burning of the Union flag at the memorial to the Glencoe massacre, an event it blames on the "evil union" and the "Anglo-British state". A video of the SRSM's 2010 trip to Glencoe shows supporters wiping their feet on the flag.
After claiming Scottish soldiers are being sacrificed in Iraq and Afghanistan for "England's glory", a speaker explains: "We stand on the Union Jack because it's a flag we despise, because it's a bloody butcher's apron that has been used to subjugate not only the Scottish people but peoples of all colours and creeds across the planet. As Scots we should say we want no more of this bloody Union."
The speaker then urges the gathering to support the SNP in order to "break up the British state".
Labour MP Jim Murphy claimed Salmond had been humiliated. He said: "On Friday, the First Minister cheered our athletes who competed under the British flag. The very next week he was prepared to stand next to people who delight in burning it.
"The fact that the organisers have taken fright and kicked these hardliners out does not take away from the fact that Alex Salmond and so many top SNP members were ready to give credence to these people and their outrageous views."
An SNP spokeswoman said: "Saturday's event has been organised independently. The First Minister fully supports the actions of the organisers in removing the SRSM group."
SRSM organiser Donald Anderson said the group's members still intended to attend the rally. "We do not have any intention of burning flags at the Edinburgh rally. We will be there as individuals carrying Saltires, despite Unionist objections to our national flag. The Imperialist Union flag is not called the 'butcher's apron' for nothing."
The Scottish Republican Socialist Movement burns a Union Jack at the memorial to the Glencoe massacre