Q. [When it is prohibited to cut down a tree,] would it help if I plant another similar tree to replace it in another part of the back yard?

A. Poiskim permit transplanting a tree; with its roots and surrounding earth when needed and when we can safely assume that the tree will survive in its new location, (Sheilas Yaavetz Y.D.1: 96, Chasam Sofer Y.D. 102. See Mibeis Levi (p. 58), that this is a difficult procedure that is seldom worth the effort.

Horav Shlomo Miller’s Shlit”a opinion is that planting a new similar tree or even taking a branch from the existing one, does not minimize at all the prohibitions involved, as in Halacha (e.g. in regards to Orlo) it would be considered growing a new tree, not preserving the old one. He added, that outside of Eretz Yisroel when transplanting the same tree with its roots and surrounding earth to a new location, you do not have to be concerned if at some point the tree is not in contact with the ground, as when placed on a wheelbarrow or truck.

Rabbi A. Bartfeld as revised by Horav Shlomo Miller Shlit”a