A mature tree will be pumping very large quantities of water out of the ground through the evapo-transpiration of its leaf canopy. If you remove the tree, or take significant parts of the canopy away, this water may then “accumulate” and cause the ground heave referred to. If the tree has grown to maturity near to the property it’s very likely that the two are “in balance” and removal is then far more likely to cause property damage.

Another point to be careful of is Tree Preservation Orders. If the tree is subject to such protection, you must obtain planning permission for any work on it, let alone felling it – there are big fines for violation of this type of protection, and it’s you, the landowner, who’s responsible – not the contractor with the chainsaw!

If in doubt, get a professsionally qualified and insured arboriculturist to advise.