Is it permissible to kill a brother who drinks alcohol, uses drugs, and abandons prayer, in order to end his evil and corruption, even though he is a Muslim by identity?

If your brother abandons prayer, drinks alcohol, and uses drugs, you must advise him, remind him of Allah Almighty, be patient with him, invite him to righteousness, and not despair of his reformation. You are not permitted to kill him, as the implementation of hudud (punishments) is the prerogative of the Muslim ruler or his deputy. There is no harm in shunning him if it is highly probable that a شرعية (religiously permissible benefit) will be achieved thereby.