Taking down a large tree in a confined space like a garden, takes real care and attention. Just cutting it off at the base and letting it fall will cause a lot of damage.

The professional approach is to take down the tree, one section at a time. First the branches come off, then the trunk is taken down in pieces.

Start at the bottom and remove the branches
This gradually exposes the trunk as the tree surgeon climbs the tree.
Then back down, cutting into sections as you descend.
Felling A Large Tree