While the the fool and the simple were instructive and and helpful for us to examine, the scoffer is a completely different study altogether.  Scoffers are proud and arrogant (Prov. 21:24) and mock and scorn (same Greek word as "scoff") other people.  They are incapable of discipline and correction (Prov. 9:7-8), and they are destined for condemnation (Prov. 19:29).  Since the scoffer is "an abomination to mankind", they are to be avoided (Psalm 1:1), or even more strongly, driven out (Prov. 22:10).  Ultimately, their life incurs the "scorn" of God (Prov. 3:34).

The Scoffer Notes:
1. The Disposition of a Scoffer:
    a. Arrogant Pride
    b. Hates Correction
    c. Pleasure in Others' Harm
2. The Carnage a Scoffer Causes
3. Warning Signs of Becoming a Scoffer
    a. Contempt
    b. Cynicism
4. In Relationship with a Scoffer
5. The Need of a Scoffer