Trees planted along both sides of the path in Grange Park have been almost "completely destroyed" as vandals snapped the trunks.
Three trees along Stallings Lane, Kingswinford, have been targeted – with branches also being snapped off a number of other trees.
It has led to council chiefs in the borough calling on anyone with information to come forward following the attacks earlier this month.
Councillor Karen Shakespeare, cabinet member for public realm, said: "These trees have been planted using taxpayers’ money to try and make the borough a more attractive place for us all to live in. It just beggars belief as to why anyone would want to do such a thing.
"It is wanton vandalism and a criminal offence, and councillors on both sides of the political spectrum are determined to catch the people responsible. I would urge anyone with information on either case to contact the council or the police."
Council tree experts have performed remedial works on the trees affected but they are now unlikely to reach their full growth and potential due to the vandal attacks.
Both incidents have happened this month and police have been informed, but the perpetrators are yet to be identified. Anyone with information can call the police on 101, or Dudley Council Plus on 0300 555 2345.