First off, you need to fix your scripture reference. It is wrong in both the title (which requires a mod to fix) and in the OP (which you can fix)
Secondly, you need to read the whole paragraph and not just pull one verse out of context.
9 I wrote you in my letter not to associate with immoral people; 10 I did not at all mean with the immoral people of this world, or with the covetous and swindlers, or with idolaters, for then you would have to go out of the world. 11 But actually, I wrote to you not to associate with any so-called brother if he is an immoral person, or covetous, or an idolater, or a reviler, or a drunkard, or a swindler—not even to eat with such a one. 12 For what have I to do with judging outsiders? Do you not judge those who are within the church? 13 But those who are outside, God judges. Remove the wicked man from among yourselves.
Paul is talking about religious separation. It is for the purpose of purifying the Body of Messiah. He specifically excludes unbelievers from the separation. V13 sums it up - those outside the body get judged by God (not us); and we are to judge and remove those inside the body who are immoral, etc.