Succa page 44 deals with taking the lulav and Arava on Shabbos. The Talmud tries to determine its permissibility based upon the famous paskuk about lulav: “on the day the first day.” Does this permit even on Shabbat.
Rabbi Eliezer is quoted on this page that even the preparation of the lulav is permissible. Rashi says this extends to cutting and detaching from the tree. Interestingly there is another opinion which the SD wrote about several months ago about R. Eliezer in Eruvin on page 100 about being on a tree on shabbat. he alllows you to come down.
The SD would like to weigh in. R. Eliezer when confronted with a Mitzva but potential for chilul shabbos or a slip up on Shabbos says JUST DO IT. Be confident that you will do it right. He is not going to allow a possible slip up stop his ability to act. While clearly we do not hold like this, it is not the halacha that the SD cares about, but rather the courage, the confidence and the enthusiasm he brings to mitzos. He is a Nike Jew- Just Do It.