The video posted on social media yesterday shows villagers gathered around armed fighters while one explains they are meting out God's "prescribed punishment," according to a translation by the SITE Intelligence Group.
The video shows a cleaver descending on one man's hand, held down on a tree stump, then fades until it shows a blood-splattered stump. It does not show the actual amputations.
Nigeria's homegrown extremist group wants to impose its radical version of Islamic law and recreate an ancient Islamic caliphate that encompasses Nigeria and parts of Chad, Niger and Cameroon.
Boko Haram has been carrying out raids and suicide bombings that have killed hundreds in all four countries.