Use the word deadpan to describe someone who uses no expression when speaking, such as the deadpan way some comedians deliver even their funniest jokes — which can make them even funnier.
Deadpan dates to 1928, when pan was slang for "face." So if you seem to have a "dead face" as you say something, it means your face looks very blank — no energy or animation. Deadpan is associated with sarcasm, and like sarcasm, if you use it for comic effect, there's a risk your audience won't pick up on it. Nevertheless, deadpan humor can be funny and popular — witness the success of deadpan humor in the sitcom Seinfeld.