The hornbeam tree was given to the town by personnel from the nearby RAF St Mawgan base in 1981, and bore a plaque to this effect.
But council experts judged that it was affecting a wall and lychgate of an adjacent church.
Resident Jim Suter told the local press: "As an ex-military man myself, I think it's a disgrace the council just took it upon themselves to chop a tree down that was oozing with life, and they didn't even think to consult RAF St Mawgan."
A month after the felling, the council appeared to have made no move to plant a replacement, he added.
A former town mayor, Billy Calton, claimed there was no damage to the wall, only a branch overhanging the pavement.
But current mayor Paul Wills said the council took the action based on advice from a county tree officer.
"The tree was dangerous, it was simply too big for the area that it was planted in and it was likely to severely damage the wall by the lychgate, and it was on their advice that we took it down," he said.
He added that is was "absolutely the intention" for the council to provide a replacement.