This is the third year in a row that such damage has appeared on trees in the gardens located in the Blackpill area of the ward.
Cllr Tyler-Lloyd said: "Unfortunately it appears that trees are being targetted in our area once again.
"They have not been completey destroyed like others have in previous years, but it is so mindless. I could understand if people were chopping down trees for wood, but they are not. It is such a shame, and Clyne is such a beautiful place"
The councillor, who also sits on Mumbles Community Council, added: "I am not sure what we can do about it, except to ask everyone to be on alert.
"I would request that if anyone sees anything suspicious they report it to the police so that they can continue to look into this matter."
Cllr Tyler-Lloyd featured in th South Wales Evening Post, on 2 May 2014, discussing the damage to the trees in her ward of Mayals.