Can one fulfill the mitzvah of arbah minim if they are still attached to the tree? Or, is it lacking in לקיחה – the taking, and not consideredולקחתם - a proper taking?
The Tzlach (Shabbos 131b) writes that when it comes to the mitzvah of lulav it is not possible to have chillul Shabbos involved in the guf hamitzvah [body of the mitzvah], as even if it is still connected to the tree, there is no need to detach it, as even if one used it whilst still connected to the tree one fulfills the mitzvah.
From the Reshash (Succah 42b) it’s also clear that one can fulfil the mitzvah of arbah minim even if they are still attached to the tree.
The Pri Megodim (Orach Chaim 653) is in doubt.
The Bikuray Yaakov (651:30) writes that if one takes daled minim whilst they are still attached one doesn’t fulfil the mitzvah as it says ולקחתם – “to take”, and if it is still connected to the tree, it’s not considered taking.
He cites the Gemara in Chullin (16) which learns from the pasuk:ויקח את המאכלת – “he took the knife” that shechitah is disqualified if knife is still attached to the ground. We see that when the pasuk says an expression of “taking”, it must be detached.
However, he says, in the end the Gemara falls off this drosha, therefore, we have no proof.
He concludes: If one shook arbah minim whilst still attached to the tree, one should do the mitzvah again after they are detached. However, it’s not so simple that one didn’t fulfill the mitzvah the first time, therefore, a berachah shouldn’t be said. (For more on this shailah, see Minchas Pitim, R’ Meir Arik, Orach Chaim 651, Da’as Torah, Orach Chaim 651, and Shu”t Pnei Mavin, Orach Chaim 215)