Why is everyone suggesting using electric gel and Winter Blast, things like that, when he says that he has no ammo and no mana- err, eve. Anyway, yea just wrench him to death while you keep respawning at a Vita chamber, guess that's the only option you have left. Or load a save-game.
Anyway, I think you mean the first Big Daddy you come across, I killed that by hacking all the turrets first, then equipping armor piercing ammo and using my lightening plasmid.
PS: The ammo will get better, too good almost, when I was...halfway through the game I guess, all my guns were almost constantly full.