'Cutoff' in the Bible

I am the Vine; you are the branches. The one who remains in Me and I in him bears much fruit, for [otherwise] apart from Me [that is, cut off from vital union with Me] you can do nothing.

If a man does not keep himself in me, he becomes dead and is cut off like a dry branch; such branches are taken up and put in the fire and burned.

Then Simon Peter having a sword drew it, and smote the high priest's servant, and cut off his right ear. The servant's name was Malchus.

One of the servants of the high priest, being his kinsman whose ear Peter cut off, saith, Did not I see thee in the garden with him?