Can't I just laugh till it hurts?
A dominatrix is a person who consensually inflicts pain on people who have a particular fetish for experiencing pain. Here, the clown does not have that fetish for physical pain, and instead, is asking if he can laugh until it hurts, instead of undertaking the usual physical pain from the dominatrix, e.g., being whipped. It's funny because of the juxtaposition of physical pain and laughing pain.