Gemara

Beraisa - R. Dosa: I testify that Chagai the Navi said in this place that in Amon and Moav we separate Ma'aser Oni in Shmitah.

Many cities were conquered by Benei Yisrael that left Mitzrayim, but were not conquered by the exiles that returned from Bavel; The first Kedushah of Eretz Yisrael was not permanent. The returning exiles left over cities without Kedushah so they could be (farmed and) a source of food for the poor in Shmitah.

Yadayim 4:3 - Question: Which Ma'aser do we separate (after Ma'aser Rishon) in Amon and Moav in Shmitah?

Answer #1 (R. Tarfon): We separate Ma'aser Oni.

Answer #2 (R. Elazar ben Azaryah): We separate Ma'aser Sheni, like in most years.

R. Tarfon: Amon and Mo'av are Chutz la'Aretz, just like Mitzrayim. Therefore, we separate Ma'aser Oni there in Shemitah, just like in Mitzrayim.

R. Elazar ben Azaryah: Bavel is Chutz la'Aretz, and we separate Ma'aser Sheni there in Shemitah. The same applies to Amon and Mo'av!

R. Tarfon: Mitzrayim is close to Eretz Yisrael, therefore Chachamim decreed Ma'aser Oni in Shemitah, to help the poor in Eretz Yisrael. The same applies to Amon and Mo'av!

R. Elazar: Rain is withheld for not giving Ma'aser - "Ba'Meh Keva'anucha ha'Ma'aser veha'Terumah" (this discusses Ma'aser Sheni, which is Kodesh, like Terumah)!

R. Yehoshua: Ma'aser was enacted in Bavel long ago, by Nevi'im. Ma'aser was enacted recently in Mitzrayim, by Chachamim. It is more reasonable to learn Amon and Mo'av from Mitzrayim, for they are also a recent enactment of Chachamim!

Chachamim voted and decided that we separate Ma'aser Oni. When R. Eliezer was told, he said the vote was correct but unnecessary, for he heard from R. Yochanan ben Zakai that this is a tradition from Sinai.

Rosh Hashanah 15a - Rabah: If an Esrog had Chanatah in Shishis (the sixth year) and it entered (was picked in) Shemitah, it is exempt from Bi'ur (eradication when it is no longer available for Chayos in the fields). If Chanatah was in Shemitah and it entered Sheminis, it is exempt from Ma'aser but Bi'ur applies to it.

Question (Abaye): I understand your latter law. You are stringent (even if you are unsure whether or not it has Kedushas Shemitah, you obligate one to make it Hefker, therefore it is exempt from Ma'aser). But your first law exempts from Bi'ur. You must be sure that we follow Chanatah. If so, Ma'aser should apply to it!

Answer (Rabah): (Even if one does not make it Hefker,) everyone handles it (when they enter fields to take other fruits), therefore it is exempt from Ma'aser (like Hefker).

Bava Kama 94a (Beraisa): If one declared his vineyard Hefker and harvested it, he must leave Peret, Olelos, Shichchah and Pei'ah for the poor, but he is exempt from Ma'aseros.

Gitin 36a - Abaye: The Mishnah of Pruzbul is like Rebbi, who says that cancellation of loans in Shemitah is only mid'Rabanan nowadays.

Beraisa - Rebbi: "This is the matter of Shemitah - Shmot (refrain)". The verse discusses two Shemitos - of money (not collecting loans), and of land (Rashi - not working the land in Shemitah; Tosfos - returning sold land to the seller in Yovel);

(Tosfos - in an era) when Shemitah of land applies, Shemitah of loans applies. When Shemitah of land does not apply, neither does Shemitah of loans.

Rishonim

Rambam (Hilchos Matanos Aniyim 6:5): In Shemitah year everything is Hefker, so Terumos and Ma'aseros do not apply at all. In Chutz la'Aretz there is no Shemitah of land. In Mitzrayim, Amon and Mo'av, which are close to Eretz Yisrael, we separate Ma'aser Rishon and Ma'aser Oni in Shemitah, to support the poor in Eretz Yisrael in Shemitah. Regarding Amon and Mo'av this is a tradition from Sinai. In Bavel we separate Ma'aser Sheni in Shemitah, like most years.

Rashi (15a DH Omar Lei): The Hefker imposed by Shemitah exempts from Ma'aser. The Mechilta expounds "V'Ochlu Evyonei Amecha v'Yisram Tochal Chayas ha'Sadeh" - just like there is no Chiyuv to tithe what animals eat in Shemitah, the same applies to what people eat.

Tosfos (Nedarim 44b DH ha'Mafkir): The Sifri expounds that a Levi gets Ma'aser "Ki Ein Lo Chelek v'Nachalah Imach". Therefore, Hefker is exempt from Ma'aser, for a Levi may take it just like a Yisrael. "V'Ochlu Evyonei Amecha..." exempts Shemitah from Ma'aser; both of these verses are needed.

Kuntres Acharonim (to Turei Even Rosh Hashanah 15a, DH v'Ulai): Tosfos did not say why both are needed. Perhaps because Shevi'is has stringencies that do not apply to regular Hefker, we could not learn from Hefker to exempt from Ma'aser.

Rashi (DH Rav Hamnuna): Rav Hamnuna holds that Shevi'is does not exempt from Ma'aser. Rather, it is exempt because it is Hefker. Unlawful handling by people in Shevi'is is Gezel; it is not Hefker to exempt from Ma'aser.

Tosfos (DH Yad): In conclusion, Rabah holds like Avtulmus, so we need not say that handling by people in Shevi'is exempts. Ma'aser is determined by when it is detached, and this was in Shemitah.

Tosfos ha'Rosh (DH Yad and DH d'Ein): Alternatively, this is even according to Avtulmus. Only which Ma'aser (Oni or Sheni) is determined by when it is detached. Shemitah mid'Rabanan does not exempt from Ma'aser (Shemitah is mid'Oraisa only if it grew entirely in Shemitah).

Rashi (Kesuvos 25a DH v'Lo Nischayvu): Ma'aser did not apply during the conquest and division of Eretz Yisrael because it depends on Shemitah ("ba'Shanah ha'Shelishis Shenas ha'Ma'aser", and Shemitah did not apply then).

Poskim

Shulchan Aruch (331:19): In Shemitah year everything is Hefker, so Terumos and Ma'aseros do not apply.

Beis Yosef (DH v'Ein): The Tur writes that Terumos and Ma'aseros do not apply in Shemitah because people do not plant. Alternatively, everything is Hefker, so whatever grows is exempt.

Rema: Some say that if a Nochri sold produce to a Yisrael in Shemitah and the Yisrael did the Gemar Melachah (final processing), Terumos and Ma'aseros must be taken. Ma'aser Oni is given, like Amon and Mo'av.

Source: Kaftor v'Ferach, cited by Beis Yosef (DH v'Ein).

Chazon Ish (Shevi'is 9:18): This is like Rashi, that the exemption of Shemitah is because it is Hefker. Peros Nochri are not Hefker. One who buys them acquires them until Bi'ur, and can use them to Mekadesh a woman. However, Tosfos holds that Peros Shemitah are always exempt. Perhaps Tosfos infers this because the Torah never specified which Ma'aser to take in Shemitah. This is not a proof, for according to Rebbi, Shemitah does not apply when there is no Yovel (Gitin 36a), even if there is Kedushas ha'Aretz for Ma'aser, and Ma'aser applies then!

Note: According to Tosfos (Gitin 36a DH bi'Zman), Rebbi does not discuss Kedushas Shemitah of produce.

Teshuvas Maharit (1:43): The exemption of Peros Shemitah is not due to Hefker. Will we say that if a Yisrael did not make them Hefker, Terumos and Ma'aseros apply to them?! The Beis Yosef suggested they have the same law as Peros Nochri, and perhaps indeed both must be tithed. This is unreasonable; the Torah made Peros Yisrael Hefker! The Gemara exempts from Ma'aser a sixth year Esrog that entered Shevi'is because everyone handles it. This is because primarily we follow Chanatah, and it is a sixth year Esrog. If it was truly of Shevi'is we would not care whether or not people handle it. Rashi says that Rav Hamnuna obligates tithing it because people have no right to handle it; Gezel does not exempt. The Sifri learns from "Shenas ha'Ma'aser" that some years, i.e. Shemitah, are exempt. It does not depend on Hefker!

Chazon Ish (continued): Also, if Chanatah of an Esrog was in Shemitah and it was picked in Sheminis, Ma'aser is according to the law of Shemitah! The Yerushalmi connotes that the exemption of Shevi'is does not depend on Hefker. However, if nowadays Shemitah is mid'Rabanan, like Rebbi, but Terumah is mid'Oraisa, then the exemption is only due to Hefker, so what is bought from a Nochri is Chayav. However, if Ma'aser ever applies mid'Oraisa to Peros Shemitah, the enactment in Chutz la'Aretz should have been made like the mid'Oraisa law. It is clear from Yadayim (4:3) that this was not done! The Maharit says that the Torah would not obligate Ma'aser in Shemitah since it results from (the exile of some Shevatim, which was) a punishment for sin. According to Rashi (Kesuvos 25a) when there is no Shemitah mid'Oraisa, there is no Ma'aser mid'Oraisa. However, perhaps Rashi only means that the obligation of Ma'aser did not begin until we started to count to Shemitah. We find that Chizkiyahu ha'Melech exhorted about Ma'aser after the exile of Gad and Reuven (which caused Bitul of Yovel, and according to Rebbi the Bitul of Shemitah).

Chazon Ish (ibid.): We follow the Rema and tithe what we buy from Nochrim. Even though the Terumah and Terumas Ma'aser cannot be eaten, this is not a problem of wasting Peros Shemitah, since one is not obligated to eat them. Even if it would be a Mitzvah to eat them, one may make a fence to guard against transgression even if it causes that part cannot be eaten. There is an Isur to leave over meat of Korban Pesach, yet Chachamim are stringent to forbid eating fat of the Gid ha'Nasheh! Similarly, Chachamim were stringent to forbid eating Sefichin (things that grow by themselves) in Shemitah. It is best to properly make Hefker what one buys from a Nochri before Gemar Melachah to exempt from Safek Ma'aser. One who is lenient like the Maharit has whom to rely on, since we rely on the Poskim who say that Ma'aser is mid'Rabanan today, all the more so regarding Yerek and fruits (that are never mid'Oraisa). However, one should be stringent about Kedushas Shemitah even regarding what grew by a Nochri. If Ein Kinyan l'Nochri (he cannot acquire land) in Eretz Yisrael to exempt from Shemitah, his produce is Hefker and hence exempt. The Beis Yosef holds that Yesh Kinyan l'Nochri as long as he has the produce. However, the Gra refuted this. The Gra also says that nowadays that Ma'aser is mid'Rabanan, Yesh Kinyan l'Nochri to exempt from Ma'aser, so one need not tithe what he buys from a Nochri in Shemitah.