Summary: Pride is a sneaky thing. It's the default program for humans and is at the root of the problem in Corinth, and often at the root of our problems as Christians.
The American Heritage Dictionary defines sarcasm as: "A form of irony in which apparent praise conceals another, scornful meaning." An example might be to someone who is always late and you say to them: "Oh my, you're right on time!"
Now if I told you that the Bible has several excellent examples of sarcasm you might say "well, no, Pastor Tom—what place would sarcasm have in the Holy Scriptures!" In fact, this section of 1st Corinthians has one of the best uses of sarcasm around.
I picture the members of the Corinthian church as balloons that are blown up really big and are floating around the church, each trying to rise higher than the other. The stuff inside the balloons is the pride of the Corinthian Christians and the method Paul uses to bust those balloons is sarcasm.
Paul is basically finishing up dealing with the first issue of the letter: that the Corinthians were using worldly values to judge the relative value of one pastor over another, claiming that their pastor was better than the others due to man-centered things like rhetoric.
In the last section we learned that it was wrong to use the world's value system to judge leaders or ministries, that the Lord Himself would be the judge. Leaders are merely managers of the gospel message. We can use one very important tool, though, in determining how to view ministries and ministers: God's Word.
While the Greek in this verse is a little difficult the meaning is pretty apparent. Paul is probably quoting a local proverb and using it to refer to the Scriptures. He may have been referring to the Bible as a whole (what they had of it by that time) or to the Scripture verses he has already quoted.
Just looking at those here is how I would characterize Paul's message:
"I will destroy the world's type of wisdom" (1:19)
"If you have to boast, boast that you know the God of the universe" (1:31)
"You really have no idea how different it is in God's kingdom" (2:9)
"You really have no idea how different it is in God's mind" (2:16)
"If you think you are so smart, you are walking into a trap!" (3:19)
Whether it was the Bible or these verses, the idea is the same: we need to use God's mindset, not worldly values when it comes to ministry.
The purpose is to avoid what was the original sin: pride, and its author: Satan.
Isaiah 14:13-14 (quickview)  You said to yourself: "I will ascend to the heavens; I will set up my throne above the stars of God. I will sit on the mount of the gods' assembly, in the remotest parts of the North. 14 I will ascend above the highest clouds; I will make myself like the Most High."
Pride says "I don't need anyone or anything. I'm something special in my own right and I deserve everything and will not be accountable or serve anyone but myself."
In our default human condition we buy into that line of thinking hook line and sinker because it was inserted into our DNA by Lucifer in the Garden of Eden.
What's the purpose of all this?
Paul is in effect saying "So smarty pants, who died and made you king?" What did you get that you earned? Salvation? True wisdom? God's character? Jesus said "Apart from Me you can do nothing" (John 15:5 (quickview)  ) and He meant it! They were so arrogant that they were in danger of thinking they had accomplished these things themselves.