I've hit two whitetails and an impala in the liver and all died within 100 yards. All were dead within a few minutes as well.

If you hit the liver you are a little far back. Like others have said depends on where in the liver you get them. Punch them through the center and its as good as a double lung, catch the edge of it and they will likely take a long time to die.

It does filter the blood but the major vessels in the liver are veins, not arteries, filters on the low pressure side. The portal vein and caudal vena cava are the two major ones. Cut either and the deer will die in short order. Miss them and it will take a while.