Tail vein or caudal vein is the largest vein in vertebrate animals' tail. It leads directly into the posterior cardinal vein in the posterior trunk in fishes. Mammal caudal vein (the middle caudal vein) leads to inferior vena cava.
The process does not require the death of the mouse, that is, assuming that not too much more than the established standard of "no more than two blood samples are taken per session and in any one 24-hour period.". "The lateral tail vein is usually used and 50 ul to 0.2 ml of blood can be obtained per sample depending on the size of the animal." 
Warming the animal to an ideal 39 degrees C may be a necessary to cause the dilation of the veins and allow for easier processing.