There aren't a lot of descriptions of the effect of necrotic damage, but I found these:
Blight: Necromantic energy washes over a creature of your choice that you can see within range, draining moisture and vitality from it
Abi-Dalzim's Horrid Wilting: You draw the moisture from every creature in a 30-foot cube centered on a point you choose within range
Harm: You unleash a virulent disease on a creature that you can see within range....On a failed save, it takes 14d6 necrotic damage, or half as much damage on a successful save
I would say most things killed by necrotic damage will have the "withered corpse look" (skin covering bones with nothing in between, a few strands of white hair left on the head, etc.).
Spells do what they say they do, unless the DM is agreeable. I would be disinclined to start targeting limbs, ect. in the middle of the campaign. Also, what the PC's can do, NPC's can do, so if the PC can necro-zap the ogre's arm off, the lich can do that to a PC barbarian's arm too. As a DM, I would want buy-in before doing that.