Sukkah, Chapter 1, Mishnah 4. This mishnah deals with the laws of invalid sechach - various kinds of covering that are not fit for use as the roof of a sukkah.
Training a vine, a gourd, or ivy over the sukkah:
The Mishnah teaches that if a person trained a vine (a grapevine), a gourd (a type of squash), or ivy (some translate it as a climbing shrub) over his sukkah, and then laid sechach on top of them, the sukkah is invalid. The reason: all of these are attached to the ground and grow from it, so the sukkah turns out to be covered with a mixture of valid sechach and invalid sechach, and therefore it is not fit.
The Mishnah, however, qualifies this, and lists two ways in which the sukkah can be made valid:
Adding a great deal of valid sechach: when the quantity of valid sechach far exceeds the invalid sechach that is attached to the ground, so that the invalid sechach is nullified by the majority and is no longer noticeable.
Cutting it from the ground: since its entire disqualification stems only from its being attached to the ground, once it is cut off from the ground the reason for the disqualification falls away.
"Ta'aseh v'lo min he'asui":
The Gemara clarifies that even if he cuts the invalid sechach from the ground, the sukkah does not become valid on its own, because of the disqualification known as "ta'aseh v'lo min he'asui" - "you shall make it, and not from that which is already made." A person must actively make the sukkah - "ta'aseh" - and it is not enough to rely on something that already came into being on its own and was only rendered fit after the fact.
An example of this: someone had a stack of straw, and there was not enough space inside it to be considered a valid sukkah, so he hollowed out a space within the stack until walls were formed from the stack and the covering was already in place above - this is "ta'aseh v'lo min he'asui," and it does not work. For he did not place sechach on top of walls; rather, what stood before him was not even considered sechach at all, since straw is called sechach only when it is placed on top of walls. Here the sechach came into being on its own, and therefore it does not help.
The same applies in our case: he had invalid sechach in place, and by merely cutting it he did not make a sukkah out of the sechach. Rather, he took something that was already lying there and turned it from invalid sechach into valid sechach, but there was no act of placing valid sechach on the sukkah at all.
Therefore, in order to make it valid, an additional act is required, and this is what the Mishnah means when it says "shek'taman" - that he cut them: afterward he must lift up the ivy or the vine that he cut and set them down again for the sake of valid sechach, and then the sukkah is valid. It emerges that an actual act of placing for the purpose of covering is required, and it is not enough that it has become a type of valid sechach.
"Zeh haklal":
Now the Mishnah gives a comprehensive rule for the laws of valid sechach: "Zeh haklal: kol shehu mekabel tumah v'ein gidulo min ha'aretz - ein mesachechin bo; v'chol she'eino mekabel tumah v'gidulo min ha'aretz - mesachechin bo" - "This is the rule: anything that is susceptible to tumah and does not grow from the ground - one may not use it for sechach; and anything that is not susceptible to tumah and does grow from the ground - one may use it for sechach." The letter vav in the word "v'ein" means "or," that is, either one of the two disqualifications is enough.
"Mekabel tumah" - something susceptible to tumah, such as a utensil and the like, which is capable of becoming impure, even if it is not actually impure at the moment.
"Ein gidulo min ha'aretz" - that it does not grow from the ground.
Anything that has one of these disqualifications may not be used for sechach. In contrast, something that possesses both qualities together, that it is not susceptible to tumah and also grows from the ground, may be used for sechach. From here we learn that food, even though it grows from the ground, is not fit for sechach, since it is susceptible to tumah.
In summary: in this mishnah we learned that one who trains a vine, a gourd, or ivy over his sukkah and lays sechach on top of them has an invalid sukkah, and that there are two ways to make it valid: adding a great deal of valid sechach that nullifies the invalid, or cutting it from the ground. We also learned that cutting alone is not enough, because of "ta'aseh v'lo min he'asui," and that lifting the sechach and setting it down again for the sake of covering is required. Finally, we saw the general rule: anything that is not susceptible to tumah and grows from the ground is fit for sechach.