The whole thing is unfamiliar - I had no idea Briggs and Stratton offered a threaded crankshaft as an option. I suppose it is possible that the purpose of the nut is to locate the clutch axially (keep it from moving toward the engine). You might try holding the flywheel so it can't rotate and tightening the nut against the clutch: that might push it off the crankshaft. It might be a sort of built-in puller.
