Gemara

(R. Zeira): When Yom Kipur is on Shabbos, Kenivas Yerek (cutting vegetables, or perhaps rinsing them) is forbidden.

Support (Rav Mana - Beraisa) Question: What is the source that when Yom Kipur is on Shabbos, Kenivas Yerek is forbidden?

Answer: It says "Shabason" - cease.

Question: What [kind of Kenivas Yerek] does this teach about?

Suggestion: It forbids Melachah [of Kenivas Yerek, e.g. it was attached].

Rejection: It explicitly says "Lo Sa'aseh Chol Melachah"!

Answer: It forbids Kenivas Yerek [that was already detached].

(R. Yochanan): Kenivas Yerek is permitted [after Minchah].

Question: The Beraisa refutes this!

Answer (and defense of Suggestion): Really, "Shabboson" adds an Isur Aseh in addition to the Lav forbidding Melachah.

150a: "Mi'Mtzo Cheftzecha v'Daber Davar" - your desires are forbidden, but Shamayim's desires (Mitzvos) are permitted.

Rishonim

Rambam (Hilchos Shabbos 21:1): "Tishbos" obligates ceasing even from things that are not Melachah. Chachamim forbade many things due to Shevus. Some resemble Melachos, and some are decrees lest one come to an Isur Skilah.

Magid Mishneh: The Rambam means that the Torah forbade Melachos, but a person could toil the entire day in matters that are not Melachos. Therefore, the Torah said Tishbos. The Ramban (brought below) said so. Chachamim forbade many matters. Or, perhaps the Rambam means that Shevus has a support from the Torah, from Tishbos, like the Beraisos in the Mechilta (the Halachic Midrash on Shemos).

Lechem Mishneh: The Magid Mishneh's first Perush is that "Tishbos" forbids Shevus. The Torah authorized Chachamim [to decide what is Shevus]. The latter Perush holds that the Torah forbade only proper Melachos. Chachamim used the verse to support Shevus. This is difficult, for the first Perush holds that all Shevusim are mid'Oraisa. The opinion that the Torah forbids Melachah on Chol ha'Mo'ed holds that the Torah forbade Melachah [on Chol ha'Mo'ed], and authorized Chachamim [to decide which are forbidden]. Rather, the first Perush holds that the Torah forbade total Melachos, but only the full Shi'ur. "Tishbos" includes even what is not a Melachah, i.e. to be liable for it (i.e. Chetzi Shi'ur). He says that Chachamim forbade many things. This is not in the category of Shevus. It is a separate matter. The latter Perush is like I said above. This Perush is correct, and corresponds to his words.

Rambam (24:12): Chachamim forbade moving certain things on Shabbos like one does on weekdays. Nevi'im commanded that one's walking and talking on Shabbos must be different than during the week, like it says "v'Daber Davar." Chachamim reasoned that all the more so, one should not move [things] on Shabbos like on weekdays, lest the day be profane in his eyes. He might come to lift and adjust Kelim from corner to corner or from house to house, or hide away rocks and similar things, since he is idle and in his house the entire day, and seeks to be occupied with something. It will turn out that he did not rest! This would negate the Torah's reason "in order that he rest."

Rambam (13): Some people do not have jobs. They are always idle from Melachah. If it would be permitted to walk, talk and move things on Shabbos like on weekdays, Shabbos would not be recognized.

Ramban (Vayikra 23:24): The Mechilta expounds "u'Shmartem Es ha'Yom ha'Zeh" to include Shevus, which is not Melachah. One might have thought that this applies even to Chol ha'Mo'ed. "Ba'Yom ha'Rishon Shabboson..." refutes this. If this is an Asmachta, why does it discuss "Shevus", which always refers to mid'Rabanan laws? How can we seek a verse for laws mid'Rabanan? Asmachtos say that the law is from the Torah. We do not say 'what is the Torah source for this mid'Rabanan law?' I say that the verse commands resting on Yom Tov even from matters that are not Melachah, and not spend the entire day measuring grain, weighing Peros, filling barrels, and doing business. Another Mechilta of R. Shimon expounds from "Kol Melachah" Melachos for which one is not liable, such as alighting on a tree, riding on animals, swimming... "Shabboson" forbids Shevus, i.e. Mitzvos such as declaring Hekdesh or separating Terumah. Perhaps both of these are an Asmachta for Shevus. The Torah forbids Melachah with a Lav on Yom Tov. On Shabbos there is also Kares and Misah. On both of them, it forbids exertion with an Aseh. The Navi says "me'Asos Derachecha mi'Mtzo Cheftzecha v'Daber Davar." Chazal expounded that Shevus does not apply to Chol ha'Mo'ed. This is mid'Oraisa. Mid'Rabanan, whatever one may not do, he may not tell a Nochri to do it.

Kuntres Divrei Sofrim (in Kovetz Shi'urim, 1:17): The Rambam does not mean that he transgresses an Aseh. That is only for Melachos forbidden on Shabbos, but not for moving rocks from one corner to another. Rather, it is against the Torah's desire, even though there is no specific command on this.

Addendum: One could explain the Rambam like the Ramban, that the Torah commands to refrain from matters that are not Melachah. This requires investigation.

Ritva (Rosh Hashanah 32b DH u'Verem): We always discuss Shevus mid'Rabanan, but there is also Shevus mid'Oraisa. If not, stores would be open, and also storehouses of grain and wine, and people would carry from house to house through Karmelis, and measure, weigh and count. It is unreasonable that the Torah forbids Hotza'ah [of food to Reshus ha'Rabim] the size of a fig, and permits this great exertion. If so, this would not be a day of rest! Rather, the Mitzvas Aseh of the Torah of Shevus is to cease from all Melachos, lest Shabbos be like a weekday. However, every detail, if he guards it and he is careful about the rest, is only mid'Rabanan. Because Shevus has a source mid'Oraisa, Chachamim were stringent about it to override Torah Mitzvos. This beautiful Chidush is from the Ramban.

Rashi (114b DH Asur): Kenivas Yerek is forbidden not only on a regular Shabbos due to Shevus, for he toils for the sake of a weekday. When Yom Kipur is on a weekday, other Shevus is forbidden, but we permit Kenivas Yerek due to Inuy. Even so, when Yom Kipur is on Shabbos, Chachamim did not permit it.

Tosfos (114b DH Ela): The Ri says that the Beraisa is a mere Asmachta. If it were mid'Oraisa, it would forbid also on Yom Kipur. On 73b we say that one is liable for Kenivah of beets. That is when they are attached. One is liable for Prisah (dicing) beets. That is due to grinding, when he makes the pieces very small. Here we discuss making big pieces.

Acharonim

Chasam Sofer (Teshuvah 6:97): Regarding trains, we are not concerned for Nochrim doing Melachah (burning coal), since mostly Nochrim use them (so they do so for the sake of Nochrim). The only concern is leaving the Techum. The Rif, Ramban and Ba'al ha'Ma'or say that there is no concern for Techumim regarding a boat. However, there, one cannot get off before Shabbos. We cannot bring a proof to permit on a train, for one could get off before Shabbos. Do not say that going for the needs of income to support his family is like a Mitzvah, which we permit. Chachamim permitted going to the end of the Techum only for Mitzvos such as needs of a Mes or Kalah. Even though one may go there on Shabbos, since he does an action with his body [for something forbidden on Shabbos, e.g. to bring Peros], this is included in "mi'Mtzo Cheftzecha..." This is a Torah Isur, like the Ramban says. Rather, sitting on a boat is different. It is like sitting in his house. He does not do anything with his body. The water moves him, and he rests. One who goes to the end of the Techum transgresses "Im Tashiv me'Leches Raglecha", and he is not Shoves. This is more Uvda d'Chol (a weekday activity), and he transgresses Shevus mid'Oraisa. On a boat, one sits and can engage in Oneg Shabbos just like in his house. This is not so on a train, for his body moves back and forth. If he travels for business, this is worse than heading to the end of the Techum. It is forbidden, and it is mid'Oraisa according to the Ramban.

Tzitz Eliezer (1:21): Also the Rambam holds like the Ramban, according to the Magid Mishneh's first Perush. Rashi explains that Kenivas Yerek is mid'Oraisa, but Tosfos says that it is an Asmachta. R. Yochanan holds that "Shabboson" adds an Aseh for Melachah. Rashi holds that R. Mana disagrees, and expounds Shevus to forbid Kenivas Yerek mid'Oraisa. The Mechilta supports him. This is why the Rambam (Hilchos Shevisas Asor 1:3) and Shulchan Aruch (OC 611:2) rule like him. Tosfos holds that all agree that it is mid'Rabanan.

Mishpetei Uzi'el (OC 9): The Rema (305:18) forbids sitting on a wagon driven by a Nochri, for he uses an animal, and lest he break a branch. He did not forbid due to Shevus! This is difficult for the Chasam Sofer.

Answer (Tzitz Eliezer): The Mechilta and Ramban support the Chasam Sofer. Further, the Rema's reason of using the animal is included in Uvda d'Chol. The Yerushalmi says that if one is riding on an animal, we tell him to descend, for it says "Lema'an Yanu'ach Shorcha v'Chamorcha Kamocha." The Yam Shel Shlomo explains that we are not concerned for the animal resting from Melachah, for riding is not a Melachah, since a living person carries himself. Rather, it is to spare the animal pain, so it may rest. The Chasam Sofer says that this is like the Ramban, who forbids exertion even if it is not Melachah. The Korban Nesan'el (on Rosh Eruvin 4, Sa'if Katan 10) says that due to Tza'ar Ba'alei Chayim, he transgresses Lema'an Yanu'ach. We can say so according to the Rema. The animal suffers more than the person does. The Rema gave the details. The general rule is that the animal must rest.

Avnei Nezer (OC 133:3): Someone said that even though mid'Oraisa, the Aseh of Shabboson applies only to Melachos, the Rambam says that mid'Rabanan, Tishbos mandates resting even from matters that are not Melachos, including Techumim. I say that since mid'Oraisa it applies only to Melachah, mid'Rabanan it applies only to what resembles Melachah, or can come to Melachah. Therefore, for each Melachah, the Rambam detailed the Shevusim that pertain to it. Techumim are not due to Melachah. There is an Asmachta from "Al Yetzei Ish mi'Mkomo." The Ran at the beginning of Shabbos says that Chachamim did not forbid due to Shevus things like removing bread from an oven, which is a Chachmah, and not a Melachah. This implies that what Chachamim forbade is considered Melachah.

Minchas Chinuch (297:1,2): Even though the Rambam wrote regarding Shabbos that Tishbos forbids exertion, and he did not say so regarding Yom Tov, it seems that he holds that the same applies to Yom Tov. "Shabboson" connotes like this. Even though the Torah says Shabboson only regarding Rosh Hashanah and Sukah, but not regarding Pesach and Shavu'os, all the Mo'adim are equated to each other.