May one cut the branch of a fruit tree to use as a decoration for Shavuos?
Background of the custom to place plants and trees in one’s home on Shavuos: It is customary to spread plants and trees in Shul and home in honor of Shavuos. Plants are spread in remembrance of the joy of Matan Torah. Fruit trees are entered into the home being that fruits of the trees are judged on Shavuos and we thus place them in Shul and in our homes in order to remember to pray for their good judgment.
The law regarding cutting branches off fruit trees: It is forbidden to destroy a fruit bearing tree without a Halachically valid justification due to the Biblical prohibition of Baal Tashchis, as well as due to danger. Accordingly, some Poskim rule it is forbidden to break a branch off from a fruit bearing tree [without one of the Halachically justifiable reasons that permit uprooting fruit trees]. Other Poskim however rule it is permitted to be done [in all cases]. Other Poskim are lenient for the sake of a Mitzvah. Practically, one may be lenient for the sake of a Mitzvah through asking a gentile to cut it off. [Thus, if one needs to cut branches for Shavuos decorations, ideally one should cut the branches of a non-fruit bearing tree. If this is not available, then he is to ask a gentile to cut the branches.]
Pruning branches off a tree for maintenance purposes: It is permitted to prune branches off a fruit tree for the purpose of benefiting the health of the tree, so it grows healthy fruit, in accordance to the directives of a professional gardener. However, it is forbidden to prune the branches simply for beauty purposes, to beautify the tree. Furthermore, even when pruning for purposes of maintaining the health of the fruit tree, it is best for it to be done through a gentile, such as a gentile gardener, as stated above.
 See Admur 494:14-15; ; Rama 494:3; Maharil Shavuos; M”A 494:5; Chok Yaakov 494:7; M”B 494:10
 See Darkei Teshuvah 116:51; Piskeiy Teshuvos 629:12
 The justifiable reasons: It is permitted to cut down a fruit bearing tree in any of the following cases: 1) One needs the space of the tree for building purposes. 2) The tree is blocking the sun from one’s window, [and it does not suffice to simply trim the branches]. 3) The wood of the tree is worth more than its fruit production. In all cases of allowance, one is to initially have a gentile cut the tree to avoid all worries of danger, and if one is able to uproot the tree with its roots and soil, and replant elsewhere, then he is obligated to do so. [See Admur and Poskim ibid; Sheilas Yaavetz 1:76, brought in Darkei Teshuvah 116:51]
 Admur Shemiras Guf Venefesh Baal Tashchis Halacha 16-17; Bava Kama 91b-92a; Bava Basra 26a; Makos 22a; Pesachim 50b; Semak 229; Rambam Melachim 6:10; Tzava of Rav Yehuda Hachassid 45 and Sefer Chassidim 53; Taz Y.D. 116:6; Beir Heiytiv 116:8; Pischeiy Teshuvah 116:6; Taz ibid writes that this law is omitted in Tur and Shulchan Aruch, however see Tur Y.D. 349-350; C.M. 383; See also Avodas Hagershoni Y.D. 116 and Shvus Yaakov 1:159 who question this assertion of Taz; See Shivim Temarim 53
 Beir Sheva, brought in Mishneh Lamelech Issurei Mizbeiach 7:3; Mahariy Besen 118; Beis Yitzchak 1:144
 Mishneh Lamelech Issurei Mizbeiach 7:3; Beis Yaakov 140, brought in Darkei Teshuvah 116:51; Sheilas Yaavetz 1:76
 The reason: As the prohibition only applies to destroying the entire tree. [ibid]
 Divrei Chaim Y.D. 2:59; Beis Yitzchak ibid; Dovev Meisharim 1:134; Har Tzevi 2:102
 Har Tzevi 2:101-102; Teshuvos Vehanhagos 1:376; Piskeiy Teshuvos 629:12
 This follows the ruling of Admur ibid that one may cut down a fruit tree if it is causing damage to other fruits trees of greater value. Thus, certainly one may prune a branch off the tree for the sake of having the rest of the tree grow healthy fruit, as certain branches suck out an exorbitant amount of the trees energy and prevent it from developing good quality fruit.