Per the rules, “it just works,” and how is up to you. There is no particular description of how the vorpal effect works in general, much less in this case, but size difference is not given as a defense against it. Vorpal is also extremely expensive, and is too random to really be worth the cost—nerfing it further is inappropriate.
So that leaves us with describing it. But it’s magic, so there are a lot of possibilities here. Any sword could behead someone (if that’s how the finishing blow would be described after going through the target’s hp); vorpal is special only because it can behead someone who otherwise wouldn’t be (because of hp, which is effectively plot armor). So it would not be outrageous if you described it as “you slash at the giant’s shin, striking deep—and with a ‘snicker-snack,’ a mirror stroke across the giant’s neck lops his head clean off.” That is the kind of weapon it is, why it is “feared.” It can cause am otherwise-impossible fatal wound.
If course, you don’t have to describe it that way. Your suggestion of a magical extension of the weapon—either it growing, or projecting a beam like a lightsaber—also works. There are probably endless other reasonable possibilities. I’d be somewhat leery of describing it as the halfling flying up to the giant, since that might have implications for movement and position that are not part of vorpal’s rules, but even that probably could work.