Sheffield City Council contractors began cutting down eight trees in Rustlings Road at about 05:00 GMT as part of a street improvement scheme.
Residents had demanded the trees remain. Three people arrested after confrontations with workers were released without charge.
Sheffield Hallam MP Nick Clegg said he was outraged by the council's action.
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Mr Clegg, the Liberal Democrat MP for the area, said the council had acted as if it were running an anti-terrorist operation.
"I do not know what planet these people are on," he said.
"Arresting elderly residents? Arresting them when they are just trying to say 'don't chop this tree down'?"
Jenny Hockey, a retired sociology lecturer, was one of those arrested.
"What can you do in that situation except exercise your right to peaceful protest and that's what we chose to do," the 70-year-old said.
"They warned us they would arrest us if we did not move, which is what they did."
Mrs Hockey was arrested alongside her friend Freda Brayshaw.
The retired teacher, 71, said: "It was just like an assault with arc lights, lots of policemen and chainsaws going up and down the road and we had no chance to do anything.
"They had a kind of barrier, a tape around trees they intended to fell and I stepped inside and stood under a tree."
The council said the work needed to be done as part of a Â£2bn scheme to improve streets and get rid of diseased, damaging or dangerous trees.
Residents said the trees were healthy and should remain.
Councillor Bryan Lodge said the work was "essential to ensure Sheffield has healthy trees for future generations".
He said: "We have made a final decision to increase the number of trees on Rustlings Road by almost 30%.
"We need to replace eight out of the 30 existing trees, but we will plant 17."
He said the work was carried out early in the morning on the advice of the police to ensure it was done safely.
South Yorkshire Police confirmed that 12 officers "provided assistance at the request of the council".
In April a High Court judge dismissed a bid for a judicial review into the tree-felling programme.
Sheffield City Council has felled more than 3,300 trees since 2012.
Angry scenes erupted when contractors arrived at dawn to fell trees in a long-running neighbourhood row.