Stephen Booth visited Brighouse Cemetery, Lightcliffe Road, last week when he made the upsetting discovery.
Mr Booth, 60, said: “I was horrified to find that my parents’ grave was piled high with several tons of clay from a grave being dug two plots away.
“They had wedged an old door against my parents’ newly-cleaned and polished headstone to hold the mud back.
“I had planted 80 miniature daffodils, which were coming through, and carefully turfed the rest of the grave.
“I am appalled and distressed as they had also trampled the crocuses which were in bloom on my wife and 27-day-old daughter’s grave.”
Mr Booth says he contacted the council, but “oozing, slimy clay” was still on the grave on Tuesday (yesterday) and was spreading sideways to other graves - one of a six-year-old girl.
The mess has now been cleared, but Mr Booth says he has had concerns about the upkeep of the cemetery for some time.
Calderdale Council has since apologised for the incident.
Andrew Pitts, Calderdale Council’s head of neighbourhoods, said: “We would like to thank Mr Booth for alerting us to this situation, and once we were made aware of the problem we contacted him immediately and apologised for any distress that this has caused.
“Unfortunately, when preparing for burials it is necessary from time to time for neighbouring graves to be affected by the resulting debris. This is something we make all grave owners aware of when they take out a plot at our cemeteries.
“When this issue does occur, we do all we can to tidy the affected plots and we will work with Mr Booth to ensure he is happy with the cleaning that is done.
“We’re sorry for the damage caused to the plants, and this is something we will also discuss with Mr Booth and we’re happy to meet him on site to arrange for new bulbs to be planted.
“We have asked Mr Booth to contact staff in bereavement services at any time if the site isn’t cleaned to his satisfaction and will do all we can to rectify the situation.”