The Hebrew verb karath means to cut, to cut off, to cut down, or to make a covenant. The phrase 'cut a covenant' (karath berit) is the standard Hebrew idiom for formally establishing a binding agreement, derived from the ancient practice of cutting animals in the covenant ceremony (Genesis 15).
Karath is the action behind every major covenant in Scripture. When God made His covenant with Abraham, the animals were cut in two (Genesis 15:10-18) and God alone passed between the pieces — signifying He bore the full weight of the covenant. The phrase 'to be cut off' from Israel was the ultimate covenant curse for breaking the law. The New Covenant, instituted by Jesus at the Last Supper, is inaugurated through His own body being 'cut' — crucified — representing the ultimate covenant sacrifice that could never be broken.