Gemara

128a (Beraisa): Bundles of Se'ah, Ezov and Koranis, if one gathered them for [animal] food, he may eat them on Shabbos, but he must cut them by hand, and not with a Kli.

155a (Mishnah): One may not [finely] cut fodder or carobs for a big (work) or small animal;

R. Yehudah permits cutting carobs for a small animal.

(Rav Chisda): Rav Huna holds that Tirchah (exertion) for [improving] food is permitted, but not Shivuy Ochel (to make something inedible into a food).

(Rava): Rav Yehudah permits Shivuy Ochel, but forbids Tirchah.

156b (Mishnah): We may cut gourds in front of animals, and a carcass in front of dogs [on Shabbos].

Rishonim

Rambam (Hilchos Shabbos 21:18): One may not dice fodder or carobs in front of a small or big animal, for it looks like Tochen (grinding). One may cut gourds in front of an animal, or a Nevelah in front of dogs, for Tochen does not apply to Peros.

Ran (32a DH Amar Rav): In a Teshuvah, the Rashba forbids cutting very finely to eat after a while. One may cut to eat immediately, like regarding Breirah. One may crumb bread to give to chickens immediately, for we permit Shivuy Ochel. Sefer ha'Mitzvos permits because Ein Tochen Acher Tochen. (Once something was ground, there is no Isur to grind it again.)

Shiltei ha'Giborim (32a:3): According to the Rashba, if the chickens will not eat immediately, one may not crumb for them. However, the Isur applies only to vegetables. Some forbid all Peros. This opinion would forbid also meat for one who cannot chew.

Terumas ha'Deshen (56): If one has hard roasted meat, and he cannot chew well, he may cut it finely with a knife. This is unlike cutting wood finely, for Tochen applies to food only if it is normally ground, e.g. wheat, barley and similar things, but not other foods. The Rosh says that Tochen does not apply to food. Several opinions say that Tochen applies to other foods. However, perhaps all agree that Tochen does not apply to meat, which does not grow from the ground.

Terumas ha'Deshen: However, I do not permit to cut meat finely to feed birds, since it is not prepared for proper eating, only to eat abnormally. Tosfos (74b DH Hai) says that Tochen applies only to beets. Perhaps he permits other foods because they do not need Tochen, for one could eat them whole and chew them. If not for this, it would be forbidden. Do not infer that one who cannot chew cooked or roasted meat may not cut it. This is wrong. We follow the majority, who can chew, even for one who cannot chew. Raw meat is not proper for anyone. Even though it is proper for dogs and Chayos, it is destined only for birds, due to its importance. Also, this pertains to the Isurim of Shivuy Ochel and toiling for food for animals, like in 155a. This requires investigation.

Poskim

Shulchan Aruch (OC 321:9): One may cut cooked or roasted meat finely with a knife.

Rema: One may not cut raw meat finely in front of birds. Since they could not eat it without this, he makes it a food. See 324:7.

Taz (9): This is astounding, like I wrote in 324:9.

Magen Avraham (11): There, we permit cutting whatever is very hard. This is unlike Olas Shabbos.

Machatzis ha'Shekel: Olas Shabbos, like the Taz, understood that the Rema forbids cutting finely due to Shivuy Ochel, i.e. like Rav Huna. He questioned this, for in 324:7 we rule like Rav Yehudah! He answered that the Rema permits only if one could have eaten it with difficulty without cutting. The Magen Avraham rejected this, for Rav Yehudah is more lenient about what is harder and cannot be eaten at all without Tikun. This is because one must feed his animals, and they cannot eat without this. The Terumas ha'Deshen said that if one cannot eat without cutting, Tochen applies mid'Oraisa even according to the Poskim that it applies only to Gidulei Karka. Also, it is forbidden mid'Rabanan due to Shivuy Ochel. This was a mere Snif (additional, secondary reason). Why is the Rema concerned only for the Snif, but ignores the Isur Torah? It seems that the Rema means that this is Shivuy Ochel, and therefore Tochen applies. If not for this, we would permit, for we permit Shivuy Ochel. In 324:7, he does not cut finely, so Tochen does not apply, only Shivuy Ochel. The Magen Avraham explains like this there.

Gra (DH Aval): The Terumas ha'Deshen said that there are problems of Shivuy Ochel and exertion for animal food, i.e. according to Rav Huna and Rav Yehudah, respectively. However, in 324:7 we rule like Rav Yehudah. If so, why does the Rema mention Shivuy Ochel? See the Taz. Even though Terumas ha'Deshen initially forbade because one cannot eat it, he did not rely on this, and wrote "also, [this pertains to Shivuy Ochel and toiling for food for animals]."

Damesek Eliezer: Perhaps the Terumas ha'Deshen should say "this pertains to Shivuy Ochel for birds (which cannot eat it until it is cut), and toiling for food for animals (which could eat it as is)."

Bi'ur Halachah (DH d'Ho'il): To answer the Taz' question, the Magen Avraham says that here the Rema forbids due to Tochen. This does not fit the Rema's words so well.

Mishnah Berurah (33): One can say that the Poskim who hold that Tochen does not apply to food say so because it need not be ground. One can eat it like it is. This does not apply here, where one cannot eat it without cutting. The cutting makes it a food, so Tochen applies. We discuss cutting for birds for later. If it is for right now, all permit, like in Sa'if 12.

Bi'ur Halachah (DH v'Einan): If they could eat it [uncut] with difficulty, Eshel Avraham (11) was unsure. In Mishbetzos Zahav (10) he was unsure whether the Heter for immediate usage is only for something that people can eat. The Gra proves that it is even for animal food, for the Rashba would have permitted cutting fodder finely for animals, if not for exertion.

Kaf ha'Chayim (55): Below (Eshel Avraham 324:3), the Pri Megadim concluded that we permit for immediate use even for animals.

Kaf ha'Chayim (56): The Rema connotes that one may cut big pieces.

Shulchan Aruch (12): One who cuts vegetables very fine is liable for Tochen.

Mishnah Berurah (38): The Shulchan Aruch holds that this applies even to what can be eaten raw.

Rema: One may not cut dry figs and carobs in front of elders. It is forbidden only regarding Peros and similar things. One may crumb bread in front of chickens. Since it was already ground, we are not concerned, for Ein Tochen Acher Tochen.

Beis Yosef (DH Tanya): A Tosefta (Beitzah 1:13) forbids cutting pressed dates, dry figs and carobs in front of elders on Shabbos.

Magen Avraham (14): For one who could chew them [uncut], it is permitted.

Bi'ur Halachah (DH Lifnei): The Magen Avraham permits for one who could eat without cutting. I disagree. The Tosefta merely discusses a typical case of cutting for elders, who can eat only if it is cut fine, but Tochen always applies to Gidulei Karka. It seems that the Gra holds like this. He learns from the Rashba that we permit for immediate use, since the only concerns were Shivuy Ochel or toil. This implies that not for immediate use is forbidden due to Tochen, even though they could eat without it. The Magen Avraham permits [for one who could eat without this] only figs and carobs. For vegetables cut finely, even he permits only at the same meal.

Mishnah Berurah (40): Some are lenient about Shivuy Ochel. We permit even for them to eat afterwards.

Kaf ha'Chayim (72): In Sa'if 9, we permit even for one who could not chew them uncut. There we discuss meat, which is not Gidulei Karka. One may cut for people before they need it, if they could eat it without cutting. However, cutting finely is permitted only at the same meal.

Mishnah Berurah (41): It is proper to make the pieces somewhat big, especially for animals. One should not toil for something that [the animal] can eat without the toil (324:7).

Rema (ibid.): This refers to cutting for later. If one cuts to eat immediately, everything is permitted.

Magen Avraham (15): Also for chickens that will eat immediately, we permit all cutting.

Kaf ha'Chayim (75): Likewise, one may cut if Nochrim will eat it immediately.

Gra (DH v'Chol): The Gemara (155a) forbids only due to toil for food. If not for this, it is permitted [since it is for immediate use].

Mishnah Berurah (44): One may cut finely for [your] chickens to eat immediately, since you are obligated to feed them.

Shulchan Aruch (324:7): One may cut a Nevelah in front of dogs only if it is hard and they cannot eat it without cutting. We do not toil for what is already prepared.

Mishnah Berurah (18): If it could eat with difficulty, also this is Shivuy Ochel, and it is permitted.

Rema: See above 321:9 regarding whether one may cut finely in front of birds.

Taz (4): Above, the Rema forbids what birds could not eat without cutting, but permits what they could not eat. This is unlike the ruling here! It seems that the Terumas ha'Deshen holds that toil is primary. He added Shivuy Ochel needlessly. It seems that birds can eat what is in pieces. Cutting finely is extra toil. Also the Terumas ha'Deshen is difficult. Since the birds cannot eat unless it is cut finely, this is Shivuy Ochel, which we permit!

Magen Avraham (5): One may not do Melachah, e.g. Tochen, for animals, even on Yom Tov.

Kaf ha'Chayim (29): The Acharonim hold like the Magen Avraham. Nesiv Chayim answered the Taz' questions.

Mishnah Berurah (20): Even though birds can eat only if it is very fine, it is forbidden due to concern for Tochen.

Bi'ur Halachah (DH v'Ayen): It sounds like the Rema refers to Nevelah, but really, he refers to Kosher meat. One may cut Nevelah very finely. This is clear from his source, the Terumas ha'Deshen. Kosher meat is destined for people or birds. Nevelah is mostly for dogs, so it need not be cut finely. We follow the majority.

Mishnah Berurah (21): Whatever he wants to feed them immediately is permitted.

Kaf ha'Chayim (30): One may not tell a Nochri to cut straw finely, for it is like Tochen. B'Di'eved it is permitted, for animals can eat it without cutting it.