Sacrifices of animals are possible only in the Temple which is destroyed now. Capital punishment is virtually impossible to do upon the rules described in Talmud. That is as far as I know.
Ethnic Israel was subject to temple laws, which included laws regarding animal sacrifice. The temple’s jurisdiction extended only to ethnic Israel. The Mosaic Law was
Israel’s law.
The Bible divides history into three ages, essentially. In the Adamic Age, mankind forsook God and fell from grace, and so wandered in the wilderness. In the Abrahamic Age, mankind, who would call itself
Israel, attempted to reconcile with God through tabernacle and temple. In the Christian Age, Israel finally did reconcile with God through their Messiah.
Jesus criticized the Pharisees because they turned the faith into the source of their enrichment and paying too much attention to an external side of the faith. The way the most Christan churches do now, frankly speaking.
In the first century, as the temple's days were numbered, ethnic Israel was becoming a heavenly Israel (or heaveny Jerusalem), as Paul and others called it, and this new, heavenly Israel reconciled with God not through temple or territory but merely through relationship, merely through Spirit, as was the case in the garden. No temple, no ritual, no edicts committed to animal skins. That’s what the Pharisees feared about Jesus (and Paul); they and their forebears invested Israel’s hope in temple and territory. Jesus said their hope was in God. The hope of Israel (resurrection) was not in the flesh; it was in the Spirit. This threatened the teaching and authority of the temple hierarchy, so they had Jesus killed.