When you first hear this, you might think, "How wise, how noble, how true". But let's actually apply a bit of critical thinking to this idea.
So let's restate the idea; you shouldn't punish anyone unless you are without sin. But Christianity teaches us that we are all sinners, and I have to admit that I'd be very surprised if you could show me any adult (apart from fictional characters) who are sinless. So the suggestion is that we should never punish anyone.
This is absurd, as is evidenced by the fact that every human culture there is the concept of crime and punishment. Punishment has three purposes. 1) it acts as a deterrent to committing future crimes, 2) in prison there are very few crimes that you can commit and 3) prison can be an opportunity for rehabilitation, to turn your life around.
So since we're all agreed that punishment for crime is a good idea, it follows that we all think that the idea "Let him who is without sin, cast the first stone" is nonsense.