In T-3, the T-850 removes its backup battery and shoves it in the T-X’s mouth. It then says “You’re terminated” while still holding on to the T-X’s wires. How did the 850 keep functioning for so long after its second battery is removed? Do terminators have a third battery?
This appears to be a filming error. In the original script (on which the film's official novelisation is based), the fuel cell seems to be still wired to the Terminator right up to the point that it exploded. Even in its damaged state it would, presumably, give out sufficient power to allow one last quip.
Without hesitation he yanked the cell out of his chest, trailing wires and mechanical parts, sparks and fluids flying in all directions.
With his free hand he grabbed the T-X by a piece of tubing protruding from her hip and dragged her back.
She turned and fixed him with a baleful gaze.
"You are terminated," he told her.
Terminator crushed the fuel cell to rupture it, and thrust it into the T-X's mouth, driving it deep into her throat.
"Eat me," Terminator said, and the fuel cell erupted with a tremendous explosion.
Endoskeleton components have emergency power sources
In Terminator: The Sarah Connor Chronicles, the head of the Cromartie T-888 retained power(1) when detached from its body and separated from the body's fuel cells:
Judging by how its eyes glowed and darkened, the head apparently had to ration its remaining energy while the body was en route to recover the head. The head's backup power supply seems to be limited.
The T-888 series is a more recent design than the T-850 from Terminator 3, but they have similar frames, and so it's reasonable to suppose that they have similar capabilities such as emergency power for their components. Even if only the head has an emergency power source, we know from the closing battle of Terminator 2 that a terminator can re-route its power supply to bypass internal damage:
It seems that a terminator's head can deliver enough power for a triumphant final taunt.
(1) And the body still had visual sensors and a robust wireless link to the CPU in the head, but I think we're supposed to forget that ever happened.
From a design perspective I wouldn't build sophisticated electronic/mechanical equipment like a murder-cyborg with just fuel cells.
For example, anything with flash RAM would want a battery for when it powers down or gets unplugged. Or the mechanical system might want something like super capacitors for very high load tasks like benching a car that the fuel cells either can't instantaneously deliver or would suffer huge loses to efficiency from the high current draw that the task requires.