Although even here, there is oddness. The Sword of Sharpness doesn't really do any more damage to you when it severs a limb than any other hit it would inflict*. You don't suffer ongoing damage from blood loss (that's the feature of another weapon, the Sword of Wounding). You don't even lose any of your maximum hp- you can be healed to full, despite missing an arm or a leg....unless you lost your head, at which point someone should scream "There Can Be Only One!!!".
*Unless a critical hit is also scored, but this depends on the edition. In AD&D, critical hits were not a core rule. Gary claimed to hate them. Of course he also claimed to dislike specific injuries, and yet here we are, talking about Swords of Sharpness...
"If hit points are meat, and I lose an arm of meat, then I should have less hit points", is what one would suppose would happen. I'm fairly certain many DM's would rule that way (along with the massive blood loss), but the rules of the game don't say this is what happens.
Heck, a character under the effect of an Aid spell in AD&D could lose a limb, only lose the 1d8 temporary hit points*, and none of their actual hit points!
*I mean, I'd like to think someone with a Sword of Sharpness would do more than 1d8 damage, but it is only +1 to hit and damage, so maybe the wielder isn't very strong and got a bad roll....