Rae Gill, 64, contacted the Derbyshire Times to voice concern about the state of the cemetery at St John the Evangelist off Kendal Road, Newbold.
Chesterfield Borough Council, which maintains the graveyard, has apologised for the mess and promised a clean-up at the site.
Mr Gill, a taxi driver, from Chesterfield, said he went to the cemetery with his partner recently to visit her mum’s final resting place.
He said they were shocked to see trees had been cut down and logs, branches and leaves were strewn across graves.
Mr Gill said: “It was an absolutely disgusting and disrespectful sight.
“The last thing people want to see when they’re going to pay their respects to their loved ones is their gravestones covered in bits of trees.
“I’d like to see an urgent clean-up there.
“Graveyards should be clean places.”
Councillor Chris Ludlow, Chesterfield Borough Council’s cabinet member for health and wellbeing, said: “We maintain the churchyard at St John the Evangelist Church in Newbold and our teams saw that work needed to be carried out to the trees and the diocese gave permission for this to be done.
“We are sorry for any inconvenience caused to people visiting the graves of loved ones while the work was carried out. We understand this must be distressing. Although we have tried to keep the mess to a minimum, it’s not possible to prevent this happening altogether.
“The site will be cleared up as soon as the work is finished.”