Gemara

2a (Mishnah): One may water a Beis ha'Shelachin (a field that must be irrigated) on Chol ha'Mo'ed and in Shemitah, either from a new or old spring. One may not water it from rainwater or from Kilon (a water channel, from which water must be drawn; alternatively, a bucket used to draw water).

2b - Question: Whether we say that watering (on Shabbos) is liable for planting or plowing, watering should be forbidden in Shemitah, for both planting and plowing are forbidden!

Answer #1 (Abaye): Our Mishnah is like Rebbi, who says that Shemitah nowadays is mid'Rabanan (and Chachamim did not forbid anything that will cause a loss):

(Beraisa - Rebbi): "V'Zeh Devar ha'Shemitah Shmot" discusses two Shemitos (abstentions): of money (not collecting loans), and of land;

Shemitah of loans applies only when Shemitah of land applies. (This shows that there are times when Shemitah of land does not apply.)

Answer #2 (Rava): Our Mishnah is even like Chachamim. The Torah forbids (in Shemitah) Avos (primary Melachos), but not Toldos (derivatives):

Question: "Uva'Shanah ha'Shevi'is...Sadcha Lo Sizra (v'Charmecha Lo Sizmor)" - Zemirah (pruning vines) is already included in Zeri'ah (seeding, for it causing new sprigs to sprout), and Betzirah (harvesting grapes) is already included in Ketzirah (harvesting, e.g. grain). Why were they mentioned explicitly?

This teaches that one is liable for these Toldos but no others.

Question (Beraisa) Question: "Sadcha Lo Sizra v'Charmecha Lo Sizmor" forbids seeding and pruning. What is the source to forbid weeding, loosening the dirt under vines, and cutting off bad grapes?

Answer: We expound "Sadcha Lo ...v'Charmecha Lo" to forbid all Melachah in the field and vineyard.

Question: What is the source to forbid (regarding trees) pruning dry and moist branches, supporting very fresh and supple trees, fertilizing, removing rocks on top of roots, covering roots with dirt, and fumigating (to chase away worms)?

Answer: "Sadcha Lo ...v'Charmecha Lo" forbids all Melachah in the field and vineyard.

Suggestion: Perhaps we forbid even Kishkush (loosening the dirt under olive trees), filling trenches with water, and digging cavities for water under vines!

Rejection: "Sadcha Lo Sizra" - Zeri'ah was already included (in "Shabbos Shabboson Yihyeh la'Aretz"). It was mentioned explicitly to make a Hekesh, and to teach that in Shemitah (only) Melachos like Zeri'ah are forbidden, i.e. Avodos that apply (both) to fields and vineyards.

Answer: The Beraisa is a mere Asmachta (all the other Toldos are only mid'Rabanan).

Question: Kishkush is forbidden in Shemitah!

(Beraisa): "Veha'Shevi'is Tishmetenah u'Ntashtah" - you abstain from Kishkush and removing rocks.

Answer: There are two kinds of Kishkush. One makes the tree healthier (it is forbidden), the other seals cracks in the tree (it is permitted).

Rishonim

Rambam (Hilchos Shemitah 1:1): It is a Mitzvas Aseh to cease from working the land and trees in Shemitah. It says "V'Shovsah ha'Aretz Shabbos la'Shem", and "Be'Charish uva'Katzir Tishbos". One who does such work transgresses an Aseh and a Lav, "Sadcha Lo Sizra v'Charmecha Lo Sizmor".

Radvaz: The Mechilta expounds that there is a Lav for anything forbidden by the Aseh.

Rambam (2): One is lashed mid'Oraisa only for seeding, pruning, harvesting and harvesting a vineyard. All trees are like vines in this respect.

Kesef Mishneh: Tana'im argue about whether or not one is lashed for plowing. Because it is a Safek, we do not lash. Also, Rava and R. Yochanan hold that one is not lashed.

Rambam (3): Zemirah is already included in Zeri'ah, and Betzirah is included in Ketzirah. They were mentioned explicitly to teach that one is lashed for these Toldos, but not for other Toldos or Avos. One is lashed mid'Rabanan for other forbidden Melachos.

Rambam (4): One who digs or plows for the sake of the land, removes rocks, fertilizes, inserts roots into the ground, grafts or plants a tree is lashed mid'Rabanan.

Ri Korkus (1): The Rambam (above, 1) said that "Be'Charish uva'Katzir Tishbos" refers to Shemitah. He often cites a verse to support a Halachah even if the Gemara rejected the support. R. Yishmael holds that this verse discusses Shabbos. However, it seems that the Rambam rules like R. Akiva, who says that it discusses Shemitah.

Question #1 (Tosfos R. Akiva Eiger Shevi'is 2:2 12): The Rambam rules that Tosefes Shemitah applies only when the Mikdash stands. This is like R. Yishmael!

Question #2 (Mayim Chayim, brought in Likutim in Frankel Rambam): According to R. Akiva, plowing is forbidden mid'Oraisa in Shemitah. Also, the Rambam forbids plowing a field of mature trees in Erev Shemitah, and Tosefes Shemitah applies only to what is mid'Oraisa in Shemitah. Why does the Rambam say that plowing is only mid'Rabanan?

Answer #1 (Mayim Chayim): Plowing is forbidden mid'Oraisa, but one is not lashed for it mid'Oraisa.

Answer #2 (Ri Korkus 4, DH Keitzad): The Torah forbids plowing to help trees grow. This is why a tradition from Sinai is needed to permit plowing a field of young trees in Erev Shemitah (Halachah 3:5). Plowing for the land, to prevent a loss, is forbidden only mid'Rabanan.

Ri Korkus (DH v'Chen): It is difficult to say that the Torah forbids plowing but permits planting trees. However, we must say so to answer why the Torah needed to mention the four Melachos (seeding, pruning, harvesting and harvesting grapes). I.e., only these are forbidden mid'Oraisa. R. Shimshon (Shevi'is 1:1) holds that planting trees is also considered seeding, but R. Tam agrees with the Rambam.

Rambam (5): We do not plant even barren trees in Shemitah.

Source (Ri Korkus and Kesef Mishneh): In the Yerushalmi (4:4), Chachamim forbid burning reeds (to improve the land). R. Shimon ben Gamliel permits, and he also permits to plant barren trees. This connotes that Chachamim forbid.

One may not cut Yevoles (callus) from trees, or remove dry leaves or branches. One may not cover its top with dust or fumigate it to chase away worms. One may not anoint soft trees with something foul to prevent birds from eating them. One may not anoint unripe figs or puncture them. One may not wrap young trees (to keep them up) or cut them, or support trees. Similarly, one is lashed for any other Avodah of trees.

Source (Radvaz and Ri Korkus): The Yerushalmi permits these in Erev Shevi'is until Rosh Hashanah. This shows that they are forbidden in Shevi'is.

Rambam (7): One may be loosen the dirt under vines. One may not Mekashkesh olive trees to make them healthier, but one may do so to seal cracks.

Ri Korkus: The Rambam holds like Rashi in Moed Katan (3a DH Yekashkesh), that Kishkush is loosening the dirt underneath. In Sukah (44b DH Stumei), Rashi says that the permitted Kishkush is to cover the roots lest they dry out, and the forbidden Kishkush is to puncture and soften the dirt above the roots. The Aruch says that Kishkush is putting fertilizer under the tree.

Rambam (8): One may water a Beis ha'Shelachin in Shemitah.

Rambam (9): One may fill trenches with water.