That is such a gross interpretation
Leviticus 17:12-13
[12]Therefore I said unto the children of Israel, No soul of you shall eat blood, neither shall any stranger that sojourneth among you eat blood.
[13]And whatsoever man there be of the children of Israel, or of the strangers that sojourn among you, which hunteth and catcheth any beast or fowl that may be eaten; he shall even pour out the blood thereof, and cover it with dust.
Stranger or not you were not to eat the blood. Has nothing to do with a limb being cut off while alive or anything.
Greetings. Just to point out something, the problem is with the English translation you are using. In Hebrew it states:
על-כן אמרתי לבני ישראל, כל-נפש מכם לא-תאכל דם; והגר הגר בתוככם, לא-יאכל דם. ואיש איש מבני ישראל, ומן-הגר הגר בתוכם, אשר יצוד ציד חיה או-עוף, אשר יאכל--ושפך, את-דמו, וכסהו, בעפר
The commandment that is being given in this part of the Torah was to the Jews and Converts to the Torah who were at Mount Sinai when the Torah was given. (Marked above in bold/blue/underline)
The statement in red and underline (
הגר הגר בתוכם)
"strangers that sojourn among you" being spoken of is a convert to the Torah who accepted the Torah and has agreed to live among Israelis/Jews and keep the Torah as a Jew. It is not talking about a non-Jew who does not live among Jews and taken on the Torah (גר) or even a Noachide, Hebrew described as (נוכרי) Nochri.