you39re-off-this-case
Explanation
The Joke
A police chief tells a detective, "You are off of this case, Sanderson!" The detective protests: "If I am off this case, I am turning in my badge, chief." The chief asks "You can do that?" and the detective confirms "Why not?" The chief then reveals the real reason: "Because this is the case about finding out who stole your badge."
The punchline is that the detective is offering to surrender his badge as a dramatic gesture, but the entire case he is being removed from is about his own missing badge -- meaning he can't turn in something that has already been stolen. His dramatic cop-movie gesture is undermined by the very crime being investigated.
The Humor
This comic parodies the classic trope in police dramas where a rogue detective is taken off a case and defiantly slams his badge on the chief's desk. Weinersmith twists this by creating a logical paradox: the badge is the subject of the case itself. The detective says "That is why it is personal" -- another cliche from cop movies -- but here "personal" literally means it is about his own belongings rather than some deep emotional vendetta.
The humor comes from collapsing two separate cop-movie cliches (being taken off a case and turning in your badge) into a single situation where they contradict each other, exposing how formulaic these dramatic scenes really are.