Paul mentions the living sacrifices without explanation, as if the readers would be familiar with the concept. Similar early rabbinic vocabulary suggests that Paul is referring to sacrifices which were given to the Temple but which were inappropriate for offering, because they were female instead of male or for other technical reasons. They could not be un-offered so, although they were sacrifices, they were kept alive as temple property till they became blemished, and any profit from them was for the Lord.
Rabbinic Reflections on Living Sacrifices at Romans 12:1
Paul mentions the living sacrifices without explanation, as if the readers would be familiar with the concept. Similar early rabbinic vocabulary suggests that Paul is referring to sacrifices which were given to the Temple but which were inappropriate for offering, because they were female instead of male or for other technical reasons. They could not be un-offered so, although they were sacrifices, they were kept alive as temple property till they became blemished, and any profit from them was for the Lord.

