No. The spell stoneskin (PHB p. 163) says in no uncertain terms that the target of the spell is completely immune to physical attacks, specifically including magically-enhanced physical attacks such as from a sword of sharpness. The vorpal sword's description even says that it is just like the sword of sharpness, except with a better bonus.
The way to understand it is: if the damage is done by physical force in any way, the attack has no effect. If it's "magical energy" that does the damage, then stoneskin provides no protection.