To set someone free from captivity is in effect to release that person from the hand, or control, of the captor. You can use this analogy to remember that "manumit" derives ultimately from the Latin noun "manus," meaning "hand", plus the Latin verb "mittere," meaning "to let go" or "send." The two roots joined hands in Latin to form the verb "manumittere" (meaning "to free from slavery"), which in turn passed into Anglo-French as "manumettre" and eventually into Middle English as "manumitten." "Manus" has handed down other words to English as well. One of them is "emancipate," which is both a relative and synonym of "manumit."
This brings to mind several passages of Scripture:
"Say, therefore, to the sons of Israel, 'I am the LORD, and I will bring you out from under the burdens of the Egyptians, and I will deliver you from their bondage. I will also redeem you with an outstretched arm and with great judgments. (Exodus 6:6)
We see in the book of Exodus that G-d does, indeed, manumit the Israelites from their physical bondage in Egypt.
For we know that the Law is spiritual, but I am of flesh, sold into bondage to sin. (Romans 7:14)
Paul tells us in the book of Romans that our flesh is sold into bondage to sin.
Wretched man that I am! Who will set me free from the body of this death? Thanks be to God through Jesus Christ our Lord! (Romans 7:24-25)
We are freed from sin and made bond-servants of G-d:
But now having been freed from sin and enslaved to God, you derive your benefit, resulting in sanctification, and the outcome, eternal life. (Romans 6:22)
To Him who has redeemed us, justified us, and sanctified us be the glory, honor, and praise forever! Amen.