So you may have to get to level 81, have some serious enchantments, and pack a ton of helth, stamina, and magika potions, but it may be possible. My dad and I killed the devine in the city on Morrowind. The difference there is that his character was level 100, and was wearing one of everything you could wear and it was all enchanted. That with the load of potions plus the mark recall spell placed at the house with even more potions allowed us to kill him. The princes in Skyrim may be marked essential, though, so it might not be possible.
Vivec (who I'm assuming you're referring to) was not a Divine (Aedra), he was a Godking, nothing more than a super powerful immortal. And Morrowind was nice enough to let us kill who we pleased.
Lorewise the Aedra/Daedra wouldn't die, their manifestation would disappear and return to their realm. Gameplay-wise, none of them exist as actual NPCs in the game (excluding one who can't be attacked where he is anyway.)