It seems to me that the only point of punishment is to dissuade?

Mostly, though it could be used to dissuade that person from repeat offense, AND/OR to dissuade others from committing that offense, AND/OR as a retribution for the act.

An example of the 2nd one would be the death penalty, there is no 'corrective' behavior option for the person, cause they be dead. This is usually marketed as a deterrent for others, however studies have shown this rarely works. Most often severe punishments like death more appropriately fall under the 3rd case above.