Assasins used needles to kill people? Yeah maybe when they were dipped in poison. You can sever the spinal chord and the heart will continue to beat for a few minutes.. Even if you severed both carotid arteries (with a needles and the windpipe it would still not be an immediate death thing.
However you drive a thick spike to someone's cerebral cortex (located in the back of the skull somewhat protected where the spinal chord meets) then you can probably kill them, and at the very least paralyze them.
But using an acupuncture needle even in that fashion would probably not kill someone, they pierce and remove small parts of the brain in brain surgery all the time, especially when dealing with aneurysms, this does not kill someone. So even if you could shove a needle all the way into the brain, chances are it would not cause immediate death.