Can I tap the {witch engine} for the mana then use {sacrifice} to get six more
Yes. Since its a targeted ability, it doesn't count as a mana ability, and uses the stack. You can activate the ability (putting it on the stack) and then use {Sacrifice} on it. Once sacrifice resolves, the witch's ability will resolve (killing a creature won't remove it's ability from the stack) and you'll get the mana from it.
RESOLVED
Over 10 mana on turn 6 all black... Dang