The JW argument against the storage of blood is a rewording of the instructions given to Israelite hunters. Wild animals don't let you walk up to them and slit their throats in the Kosher manner and methods of putting a wild creature to death from a distance (e.g. An arrow, a spear, a snare, etc.) do not adequately bleed the carcass.
Residual blood needed to be removed from the body by being poured out. The JW's have subtly reworded this obligation into the stricture, "Blood removed from the body must be poured out", which would normally preclude any and all storage of blood.
Here's an example from the 1990 brochure, How Can Blood Save Your Life?:
"Witnesses believe that blood removed from the body should be disposed of, so they do not accept autotransfusion of predeposited blood. Techniques for intraoperative collection or hemodilution that involve blood storage are objectionable to them." (Cell salvage and isovolemic hemodilution procedures have both been modified slightly to make them acceptable to JW's)
Here's an example from a 1989 Watchtower:
"We have long appreciated that such stored blood certainly is no longer part of the person. It has been completely removed from him, so it should be disposed of in line with God’s Law: “You should pour it out upon the ground as water"
The use of blood for testing purposes is rationalized via the idea that the amount of blood is small; the storage is transient and not for the purposes of consumption or transfusion anyway. (As TonusOH points out above).