…you shall not eat the life with the meat. (Deuteronomy 12:23)
Not to eat ”eiver min hachai” – that is, a limb torn from a live animal – is not only a mitzvah that Jews were commanded, it is one of the seven universal (Noachide) laws that all of mankind was commanded after the flood. This puts it right up there alongside murder and theft in the scheme of mitzvah applicability.
A brief tangent: Despite the name, the “Noachide” laws were also commanded to Adam. If they hadn’t been, how would Cain have been liable for killing Abel? For that matter, Adam and Eve actually stole the fruit of the Tree of Knowledge by eating it when it had been forbidden to them. There is some discussion as to whether or not Adam had been given all seven universal laws seeing as he was a vegetarian so that eating a limb from a living animal was a non-issue. Actually, it’s not so clear that Adam was a vegetarian. While Adam did not have permission to slaughter animals for food, perhaps, if a lion killed a sheep, Adam could have eaten the sheep. If this was the case, then eiver min hachai would have been a very relevant mitzvah, informing Adam and his descendants that it was not okay to eat a limb hacked off by a lion.
The reason for this is similar to that for the prohibition on eating blood: when a limb is severed from a living animal, it still contains the animal’s life force. This is also evident in the verse stating the prohibition to Noah: Flesh with its life…you shall not eat (Genesis 9:4). To eat a limb torn from a live animal is unspeakably cruel. Since we are what we eat, eating such a thing only reinforces the trait of cruelty.
You may think that no one nowadays, Jew or non-Jew, could possibly eat an organ cut from a living animal. You’d be wrong. “Prairie oysters,” for example, are considered a (non-kosher) delicacy. When oxen are castrated (also a problem in Jewish law), the farmers figure, “There’s no sense wasting perfectly good meat!” So there’s one example how eating a limb from a live animal is still a common practice today.
This mitzvah applies in all times and places. It is discussed in the Talmud in the tractate of Chullin on pages 101b-103b. It is codified in the Shulchan Aruch in Yoreh Deah 62. This mitzvah is #182 of the 365 negative mitzvos in the Rambam’s Sefer HaMitzvos and #90 of the 194 negative mitzvos that can be observed today as listed in the Sefer HaMitzvos HaKatzar of the Chofetz Chaim.