Everyone has Death’s phone number. Anyone can call him and make a request, but you must fulfill his request, too.
I chose to italicize his because it seems to need a bit of emphasis, and I added too as much as anything to keep the two halves of the sentence from ending with the same word and being clunky. At any rate, after but is the wrong place for a dash.
If the dash was intended to indicate a “dramatic pause,” use an ellipse there instead. Dashes are not for pauses; they’re for interruptions or abrupt changes in direction.