Our Gemara on Amud Beis quotes a verse from Vayikra (1:2):
Speak to the Israelite people, and say to them: When any amongst you presents an offering from cattle to Hashem, You shall choose your offering from the herd or from the flock.
Our Gemara derives various exclusions from the qualifiers in this verse (“from the…”, and “amongst”) to render certain animals as unfit for sacrifice, such as those used for immoral and indecent acts.
You shall bring your offering from the cattle, even from the herd or from the flock” (Leviticus 1:2). The phrase “from the cattle” is mentioned to exclude an animal that engaged in bestiality and an animal that was the object of bestiality from eligibility to be brought as an offering. The phrase “from the herd” is mentioned to exclude an animal that had been worshiped as a god. “From the flock” is mentioned to exclude an animal that had been set aside for idol worship. The additional conjunction “or,” in the phrase “or from the flock” is mentioned to exclude an animal that gores a person, killing him.
There are many levels of interpretation in the Torah, and aside from this halakhic midrash, Mei Hashiloach, offers a deeper meaning. The exclusions and forms of unfitness are referring to states of devotion and readiness of the person, who is really the entity that is the sacrifice to God. When the verse uses the phrase “from amongst you”, it hints that it is the “you”, that must be cultivated into the sacrifice. In a deeper dimension, the excluded types of animals are also a representation of forms of animalistic distortions within human nature. So if one wants to become a living sacrifice, that is living devoted to God, forms of self worship, homicidal rage, and carnality must be confronted and expunged within oneself.
Mei Shiloach notes that the first successful sacrifice brought in history was that of Hevel, and the verse has a redundancy that hints at this idea (Bereishis 4:4): “Hevel, also he, brought from the firstborn of his flock.” The “also he” indicates that the main point is that Hevel was offering of himself.
It has been said that it is easier to die sanctifying God’s name than to live by sanctifying God’s name. It is admirable to make a grand sacrifice at a moment in time, and surely there will be reward for that, yet to live in an ongoing manner of devotion and service is the essential sacrifice that furthers life and connection.
Translations Courtesy of Sefaria, except when, sometimes, I disagree with the translation 
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