When should a church remove someone from the congregation for unrepentant sin?
The church should remove someone only after first dealing with them, trying to get them to recognize their sin, confess it, and gain victory over it. If they refuse and will not repent, Paul says to put them aside until they come to their senses—removing the wicked person from among the congregation.
Les explains that God judges the unsaved world outside the church, but within the church environment Paul says to put away from among yourselves that wicked person. This removal comes only after having dealt with them, trying to get them to recognize their sin, confess it, and get victory over it. If they refuse and will not, then Paul says to put them aside until they come to their senses. Earlier context stresses going to such a person in a spirit of meekness, bearing one another's burdens, helping them overcome weaknesses, and encouraging them that there is no need to be a Christian failure or constantly live in sin.
But them that are without God judgeth. Therefore put away from among yourselves that wicked person.