I've recently marked down an answer for its off-topic sarcasm and wanted to post a link to some stated policy. I've browsed the FAQ and questions here and found no precedent for this.
Should we discourage sarcasm and off-topic quips when they are mixed in with on-topic responses?
I don't think sarcasm itself is grounds for...discouragement. It depends on its nature and use. If malevolent, that malevolence should be discouraged. If the content of the sarcasm is irrelevant to the topic then that off-topic nature should be discouraged.
For that particular question, sarcasm was the least of its difficulties. It has taken me several readings to understand what was actually attempting to be said. And the one piece of relevant content (the very last statement) is just plain poor and would be downvoted without the additional irrelevant first paragraph.
tl;dr Sarcasm is fine as long as it's helpful.
In this case, the three word "means sharp wit :)" does sort of answer the question but it's so brief, it's not very helpful. DeepYellow's comment is accurate: the StackExchange critique is off topic and was only added to make the answer long enough to submit. The critique could be easily removed by simply writing: "Quick parts means Mr. Bennet has a sharp wit." or even "Quick parts means a sharp wit.". It's submittable, but still not the finest of answers.
The FAQ does say:
Answers that do not fundamentally answer the question may be removed. This includes answers that are ... not even a partial answer to the actual question.
However, this was a partial answer. Regardless of sarcasm, the offtopic part isn't helpful and should be discouraged.
The "How to Answer" page gives guidance on what makes a great answer. Nothing specific to sarcasm, but has good advice on how to write helpful answers.
Finally, the consensus from Meta.SO is that sarcasm is generally fine, but if it's unhelpful or offensive, it's not.
