“I can see you struggling Boy, don’t hurt your brain Thinking what you’re gonna say Cause everything’s a game Always trying to calculate Trying to look smart but not too smart To threaten anything they say”
NOW we’re talking. We’re in some chicken-or-the-egg, Goku-or-One-Punch-Man territory now.
Based on Wookipedia, the lightsaber’s beam of coherent energy, while powerful, isn’t absolutely capable of cutting through anything - certain materials like ‘Maladorian iron’ are durable enough to resist it. I doubt Maladorian iron is on quite the same tier as Adamantium, and Superman effortlessly survived a laser designed to cut through that in Superman/Fantastic Four. Heck, I doubt a lightsaber burns quite has hot as the sun, and Superman uses his own comparably powerful heat vision to shave. I don’t think it can muster the strength to do it through sheer energy.
The question then becomes whether the Force - which is I understand at least lightly imbued in the blade during construction - in the same category as magic, letting it bypass his invulnerability. It’s nebulous even in the Expanded Universe whether or not the Force and magic are the same thing, so we’ll have to go by DC’s (very slightly) better defined idea of it. Magic there is generally interpreted as drawing on energies outside the boundaries of conventional reality, altering things with a power from Out There.* The Force on the other hand is framed as a naturally-occurring, universally-generated energy field, more along the lines of the emotional spectrum than what the likes of Zatanna or the Spectre do. The gray area of a few Jedi becoming g-g-g-ghosts aside, I don’t think the Force works on quite the terms Superman thinks of magic as operating in.
So yeah, I’d vote on the side of a lightsaber not being able to cut most comics versions of Superman, even if it might not be the most pleasant either. Other applications of Force powers wouldn’t be able to do the job either, other than maybe applying it to try and crush his brain, and I wouldn’t bank on that either given Manchester Black - who I think we can consider as having telekinesis on a planet-breaking scale far beyond any Jedi, given he hurt Superman in a straight-up brawl - wasn’t able to quite pull that off even when his backup had worn the big guy down. Superman > Star Wars.
In a post-Multiversity DCU, magic could reasonably be interpreted as being some kind of connection to the Sphere of Gods - even aside from that being the realm of platonic concept, most of what we think of as magical, i.e. gods, demons, spirits, faeries, pixies, etc. stem from there.