well, aside the fact that we don't really know exactly what a lightsaber is (frozen light? contained plasma? magical glow stick?) there's all sorts of problems with it. A beam of plasma itself doesn't have the ability block things, doesn't behave like a sword. and neither does a laser. or anything else.
The closest might be an electric arc. (which, is a shit load of electricity flowing through a plasma channel.) Which, conceivably could be deformed sufficiently to create a blade-like shape... but that would take a shit load of power (as in... black out an entire city for a few minutes...level of power...) so putting that into a cylinder small enough to be hand held seems... er... explosive.
this would have the advantage that it touches would stick to it, get obscenely hot, and, uh, die. It wouldn't really "cut" anything though. it has the disadvantage of shorting out on anything conductive and connected to ground. Basically... you get hit with it and it dumps most or all of it's energy into you.... at least until you turn into vapor.
Pretty sure the current fansplanation/schematic books say they're plasma contained by a mag field. And this has been the explanation for like, thirty years.
This is what causes lightsaber clashes and lets them reflect blaster bolts, and occasionally explains why Jedi don't cut their way through every door. Apparently, because reasons, some doors are magnetically shielded as well.
A precaution against vacuum? Or just cuz? Sci Fi logic either way.
Of course, if it was contained plasma, cutting through someone should, like, catch them on fire, but it mostly just seems to cleanly cauterize the wound.