Introduction to הלכות תערובות: Mixing of Permitted Foods With Forbidden Foods
The laws concerning mixtures do not at first glance seem to be of biblical origin. Upon reflection, however, we can find an allusion in the following words of Holy Scripture:
(כג) רַ֣ק חֲזַ֗ק לְבִלְתִּי֙ אֲכֹ֣ל הַדָּ֔ם כִּ֥י הַדָּ֖ם ה֣וּא הַנָּ֑פֶשׁ וְלֹא־תֹאכַ֥ל הַנֶּ֖פֶשׁ עִם־הַבָּשָֽׂר׃

(23) But make sure that you do not partake of the blood; for the blood is the life, and you must not consume the life with the flesh.

It should be noted that the verb אכל is used to designate a solid food: now, blood is a liquid, and therefore, this verb should be replaced by שתה, which means to drink.
Furthermore, in the Book of Numbers, Chapter 23, we find this sentence from Balaam:
(כד) הֶן־עָם֙ כְּלָבִ֣יא יָק֔וּם וְכַאֲרִ֖י יִתְנַשָּׂ֑א לֹ֤א יִשְׁכַּב֙ עַד־יֹ֣אכַל טֶ֔רֶף וְדַם־חֲלָלִ֖ים יִשְׁתֶּֽה׃

(24) Lo, a people that rises like a lioness, Leaps up like a lion, Rests not till it has feasted on prey And drunk the blood of the slain.

In Keritot 22, the disciples of Rabbi Ishmael teach that an exception is made for the blood that comes out in a single jet after the first blow to the animal, and this blood that falls on the sheaves is not considered as water sprinkling that could render them unusable if they come into contact with impure things.
תָּנָא דְּבֵי רַבִּי יִשְׁמָעֵאל: ״וְדַם חֲלָלִים יִשְׁתֶּה״, פְּרָט לְדָם קִילּוּחַ שֶׁאֵינוֹ מַכְשִׁיר אֶת הַזְּרָעִים.
The Gemara mentions a related halakha involving blood. The school of Rabbi Yishmael taught: “And drinks the blood of the slain” (Numbers 23:24). This teaches that the blood that is considered a halakhically recognized liquid, and therefore renders other items susceptible to ritual impurity, is only blood that is exuded after death. This serves to exclude blood that spurts out forcefully at the time of the slaughter, before the animal is actually dead. Consequently, this type of blood does not render seeds susceptible to ritual impurity.
From this phrase, we can draw the following conclusion: the blood that flows gently from the animal's wound produces the same effect on the sheaves as water sprinkling.
In Chullin 36b, we read:

אמאי והא לאו אוכל הבא במים הוא א"ל אביי עשאוהו כהכשר מים מדרבנן

Why is the animal rendered susceptible to impurity in every sense; but the slaughtered animal is not food that comes into contact with water? Apparently, even items that did not come into contact with water are susceptible to impurity in every sense. Abaye said to Rav Yosef: Rabbi Shimon holds that it is not susceptible by Torah law. Rather, the Sages accorded susceptibility via slaughter of the animal a status like that of susceptibility rendered by means of water, by rabbinic law.

And yet all the negative precepts concerning blood are expressed by the words בל תאכל and not by the word בל תשתה. We can thus conclude, from the negative precepts, that it is not only forbidden to use pure blood but also to eat any mixture containing it, even if it is only a drop.
Moreover, it does not matter whether the mixture is in the form of a paste or a juice. Since mixtures constitute actual dishes, it is not surprising that Scripture uses the word אכל to speak of blood. From all these precepts, it naturally follows that the prohibitions concerning the mixing of permitted foods with forbidden foods have their source in the Bible, and these prohibitions are due to the flavor that the forbidden food imparts to the mixture.
Let us cite some examples: Forbidden fat plunged into a pot containing permitted meat imparts a certain taste to it. This prohibition is biblical; indeed, we read in Leviticus:

(כג) דַּבֵּ֛ר אֶל־בְּנֵ֥י יִשְׂרָאֵ֖ל לֵאמֹ֑ר כׇּל־חֵ֜לֶב שׁ֥וֹר וְכֶ֛שֶׂב וָעֵ֖ז לֹ֥א תֹאכֵֽלוּ׃

(23) Speak to the Israelite people thus: You shall eat no fat of ox or sheep or goat.

You shall not eat any forbidden fat or the embryonic germ found on the egg cooked with other eggs." (See § 98.) Bones of forbidden meat are not considered in a mixture because they impart no flavor to the mixture. (See § 99.)
If an insect or an egg containing a small chick falls into a pot of permitted foods, the resulting mixture is forbidden, even if the permitted foods represent a quantity a thousand times greater than the piece that fell into the pot. This is a negative precept originating in Leviticus

(מג) אַל־תְּשַׁקְּצוּ֙ אֶת־נַפְשֹׁ֣תֵיכֶ֔ם בְּכׇל־הַשֶּׁ֖רֶץ הַשֹּׁרֵ֑ץ וְלֹ֤א תִֽטַּמְּאוּ֙ בָּהֶ֔ם וְנִטְמֵתֶ֖ם בָּֽם׃
(43) You shall not draw abomination upon yourselves through anything that swarms; you shall not make yourselves impure therewith and thus become impure.
The Talmud in Chullin 98b, states that when the egg contains a small chick, it is considered as a creeping creature. (See § 100.)
This last explanation relates to the laws concerning the presentable forbidden piece and the forbidden food that may be permitted. (See §§ 101, 102.) A mixture is permitted when the forbidden food it contains alters its flavor. (See §§ 103 and 104.) Two foods, one forbidden and the other permitted, having stayed together for twenty-four hours, are considered as cooked foods: in this case, the former must be sixty times greater than the latter. (See §§ 105 and 106.)
One must be careful not to cook eggs with their shells in a pot containing an impure thing. It is also forbidden to cook permitted food with forbidden food in the same oven. (See §§ 107 and 108.) When the mixture is composed of dry foods, some permitted and others forbidden, but both of the same nature, its use is authorized if the former outweigh the latter in large quantity; but if the forbidden food is presentable and of the same nature as the permitted food, the mixture is forbidden, even when the former is present in a very small quantity. Finally, in cases of doubt and double doubt, the established rules can be applied rather broadly. (See §§ 109, 110, and 111.)