Anyone who tells you that blood is impossible to get out of a garment doesn't know what they're talking about. Either that, or they haven't tried hard enough.
This is going to sound very odd, but I swear it's true: For a fresh, relatively small stain, spit works wonders. Seriously. Spit on the stain. There's some kind of enzyme in human spit that breaks down blood.
For stains that are old, use hand soap, laundry detergent, or plain old bar soap. Put it on the stain and scrub the fabric with your hands in fists, palms facing. Of course, this wouldn't be appropriate for a cashmere sweater, but for a T-shirt, it should be just fine, since the fabric isn't delicate. Then once you've given the shirt a good handscrubbing, put it in the washer in cold water and wash it as you normally would. But check to make sure that the stain is totally gone before putting it in the dryer -- if it's not entirely gone, wash it again. NEVER put a bloodstained garment in the dryer before the stains have been removed -- or the blood will set and you'll never get it out.