Campaigner Anne Barr told the Sheffield Star: "We protested against the felling yesterday and managed to save three trees but they came back today earlier than before to try again.
"We had to move away from the first tree we were trying to save in our non-violent direct action because the police threatened us with arrest. We are now having to stand by and watch them destroy the trees."
Amey operations manager Jeremy Willis said the ten trees "have been identified for replacement by our qualified arborists", and "are either dead, dying or causing damage to adjacent structures or the highway network".
He added: "On Bannerdale Road, the threshold for referral to the Independent Tree Panel was not reached, as less than 50 per cent of residents who responded disagreed with our tree replacement proposals."
Campaigner Dave Dillner last month called for "non-violent direct action" to prevent further felling of street trees after his legal bid to stop the programme was unsuccessful.