‘For what have I to do with judging those who are outside? Do you not judge those who are inside, while those who are outside God judges? Put away the wicked man from among yourselves.'
It is not Paul's business to act as an official judge on non-Christians, those outside the church, nor is it the church's. They can be left to the civil authorities. What he means by a judge here is one who passes a verdict which results in civil punishment. Clearly he is to pass judgment on them as being sinners and as being in need of mercy. But it is not for him in that case to exact the punishment. That is in God's hands.
But those who claim to be Christians and are in the church thereby submit themselves to the judgment of the church, and are subject to the discipline of the church. They are claiming to be under the Kingly Rule of God. Therefore they must put away the man whom he has earlier described, and all who behave openly sinfully, so that they no longer come among them living a life of pretence (1 Corinthians 5:1), but come to repentance.
‘Put away (or ‘drive out') the wicked man from among yourselves.' Or alternately ‘put away the evil (or ‘wickedness') from among yourselves'. (‘Poneron' can be masculine or neuter). For this compare Deuteronomy 17:7; Deuteronomy 22:24 LXX where the same verb is used and the remainder of the sentence follows exactly. See also Deuteronomy 13:5. Paul's words here are a command to follow that Scriptural example.
Some take the words as meaning ‘put away the Evil One from among yourselves'. But the above direct references from Deuteronomy exclude that as the basic meaning, although the idea is similar. By putting the wicked man out, and by putting away evil they are effectively putting away the Evil One. (On the other hand they are also committing them to the Satan, the Evil One- 1 Corinthians 5:5 - which demonstrates that it is not he directly who is being ‘put out').