What is the act of separating from a nation and becoming independent?

The act of separating from a nation and becoming independent is called secession or declaration of independence.

Explanation:

According to https://en.wikipedia.org/wiki/Secession, secession or declaration of independence is the withdrawal of a group from a larger entity, especially a political entity.

It is a process that begins when a group proclains the act of secession or declaration of independence; it may be a peaceful or violent movement, but its outcome is a new political entity, totally independent.

basic principles: federalism, separation of powers, checks and balances, judicial review, representative democracy, limited government, rule of law, individual rights and responsibilities, consent of the governed, majority rule, popular sovereignty, equal protection.