Repairing foundation damage due to tree roots

[mrh]

There is a full-size cherry tree with its roots growing into the side of a 100-year-old foundation, through the basement wall. The foundation is made of stone and mortar. The tree needs to be removed. Can the tree be cut down and the stump and roots left intact without damaging the foundation (basement wall, compromising the structural integrity of the Two-story house?
-mrh