In the past weeks three deer have died after being chased and attacked by dogs roaming free in the 650-acre park.
"At the end of a long winter the deer are at their lowest ebb and have used up all their fat reserves," said estate operational manger Tim Birtles.
"Any stress is often enough to kill them."
The worst incident of owners not controlling their pet dog happened last week.
A dog chased a fallow buck into the mere from Dog Wood, forcing him to swim to the other side.
Mr Birltes said the owner then walked round to the Knutsford side of the water and the buck was forced to swim all the way back.
He later died.
Last week another herd of three young deer were also chased into the mere by pet dogs.
Only one of the nine-month-old calves survived.
"They were vulnerable and the mere is at its coldest at the moment," said Mr Birtles.
A red stag has also been attacked by two dogs as he lay down.
The National Trust property is unusual in allowing owners to exercise their dogs freely in the park. But Mr Birtles wants owners to respect the parkland's 400 deer.
"It's a very popular venue and there shouldn't be these problems providing owners keep their dogs under control," he said.
If they spot trouble rangers can ask a person to put their dog on a lead or leave the park if necessary.
But Mr Birtles said they wanted to avoid such action.
"We would prefer it if people acted responsibly," he said.
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