Oaks and limes which were around 10 years old were found cut down without prior consent beside the walking and cycling route near the village of Rossington last week.
The trunks had been cleanly severed and council officers fear professional-standard tools have been used.
The incident has now been reported to South Yorkshire Police.
Sharing images of the destruction on Twitter, Doncaster Council said: "This is what we’re up against. Not just ‘us’, as in Doncaster Council. All of us. Another senseless anti-social act which, worryingly, looks to have been pre-planned and carried out with proper tools.
·"The oak and lime trees pictured were about 10 years old, established and growing well so it's all very frustrating. If you know anything about this incident on the greenway at Rossington or saw anything suspicious, please report it to us or the police."