On the quest that Septimus gives you (Transcribing the Lexicon or something) you need the blood of every type of elf.

I killed a dark elf but I didn't see any blood in their inventory.

It should give you the option to "harvest" the blood when you go to loot the body.

I was wondering this exact thing too. Then I was attacked by a group of witches and when I went to loot the body of one of them a box popped up giving the option to harvest blood. It should do it automatically given that you should have the tool in your inventory and as a quest item can't remove it.

Indeed. You're also supposed to have a quest object called "harvester"-something that allows you to do so. Check if you have that.
Otherwise, kill a few more elves (never a bad thing!) and see if it doesn't solve itself