(Mishnah): If one cuts (the end of) vines or if one cuts reeds (for firewood) - R. Yosi Haglili says that he should leave one Tefach from ground; R. Akiva says that he may cut in the regular way, with a hatchet, a sickle or a saw or anything else that he would like.

If a tree branch ripped away from the trunk, he may tie it in Sheviis - not so that it reconnect but rather that it should not get any worse.

(Gemara) (Baraisa): One who cuts reeds - if the custom is to cut with a hatchet, he should break it with his hand; if the custom is to break it with his hand, he should use a hatchet. He should cut a Tefach away from the ground.

One who cuts beams should not then smooth it and cut it like steps or vice-versa (as these are both usually done and benefit the tree); rather, he may only cut it straight.

Baraisa (R. Shimon ben Gamliel): In a place where it's customary to smooth, he may cut steps; if it's customary to cut steps, he may smooth; and he may cut even close to the ground, as long as he doesn't cut with a hatchet.

R. Yosi Haglili follows Beis Shammai and R. Akiva follows Beis Hillel.

Question: Does our Mishnah come to teach that R. Yosi Haglili follows Beis Shammai and R. Akiva follows Beis Hillel? (It's already known that R. Yosi Haglili was a student of Beis Shammai and R. Akiva was a student of Beis Hillel?)

Answer: Rather, R. Yosi Haglili was more particular that it shouldn't appear like agricultural work, so he required the cutting to be a Tefach away from the ground.