Ezra10:11-12 Now therefore make confession unto the Lord God of your fathers, and do his pleasure, and separate yourselves from the people of the land, and from the strange wives. Then all the congregation answered and said with a loud voice, As thou hast said, so must we do.
A major part of the return, reform, and rebuilding the kingdom under Ezra involved putting away the strange wives. This would be a hard thing to do, and it seemed harsh. But it was important in order to keep the faith and worship of the people of God pure. The Savior of the world was to arise and come out of these chosen, separated, and called out people.
The NT believer still does the hard but necessary work of separating himself from the world, the devil, and his own sinful flesh. It is the Holy Spirit who actually calls us by the Gospel, separates us from the world, and sanctifies and sets us apart for God. Separating ourself from worldly entanglements is impossible for us to do on our own, but the Spirit of God makes it possible and works it out in us.
We do divorce our wives, but we do put away worldly influences that draw us away from the power of the gospel unto salvation.