The bitter personal divisions emerged after Alex Salmond, the party leader, said he would support Labour's plans for a devolved Scottish parliament.
One former MP condemned his remarks as "stupid". The row comes a week before a televised debate between Mr Salmond and George Robertson, Labour's spokesman on Scotland, on its constitutional future.
On Sunday, Mr Salmond conceded he would back a Labour home-rule Bill if Labour won the next general election. Devolution was a valid "stepping stone" towards independence, he said. But Iain Lawson, a member of the party's national executive, described his comments as "unbelievable". Support for a devolved assembly "went against everything the SNP has been campaigning for over the years."
Jim Sillars, ex-SNP MP for Govan, accused Mr Salmond of being a "stupid No1 headcase" whose comments would cost the SNP vital support.
The criticism drew a sharp response from Mr Salmond. Mr Lawson, he said, was "a cross the SNP has to bear" and Mr Sillars was acting like "a reverse Eric Cantona - lunging from the terraces at players on the pitch".
Labour seized on the SNP's divisions, accusing it of "descending into anarchy".