If the pen is mightier than the sword...
If the pen is mightier than the sword, then why do actions speak louder than words?
This joke is funny because it points out a seeming inconsistency when considering two common english idioms.
the phrase "The pen is mightier than the sword" indicates that a person will have better effects by discussing solutions to problems than by fighting over them.
The phrase "actions speak louder than words" indicates that when you do something it indicates your intentions better than when you say something.
Honestly, I don't see the inconsistency - they seem to me to be different enough to not warrant comment.