There is a prohibition against destroying fruit trees (Devarim 20:19). Are there any exceptions to this rule? May one cut down a fruit tree that is damaging a nearby house?
Rambam (Melachim 6:8) writes that if the tree is causing any type of damage, one may destroy it.
While the Kaf Hachaim (YD 116:85) writes that one shouldn't destroy a fruit tree to build an extension, most poskim allow one to (See Rosh, Bava Kama 91b; Aruch Hashulchan ibid; Yabia Omer ibid).
R’ Ovadia Yosef (Yabia Omer YD 5:12:5) writes that even when it is permitted to destroy the tree, it is best to sell the tree to a non-Jew first, and let them destroy it. R’ Shmuel Wosner (Shevet Halevi 5:95) writes similarly, though adds that one should also sell him the land on which the tree grows (See Teshuvos Vehanhagos 2:729).
While the Gemara (Pesachim 50b) writes that one who destroys fruit trees will not see a good sign all his life, the poskim (Aruch Hashulchan YD 116:13, Yabia Omer YD 5:12:3, Shevet Halevi 6:112) write that when one does so in a permissible manner, one does not need to be concerned.
Why not transplant the tree? Do your best to do the job well. If it doesn't survive, would you be considered as one who destroys the tree?