What Could Cause A 1 Week Old Puppy To Have Blood In Its Poop?

Nothing good. Parasites, bacteria, infection, parvo, injury. You need to see your vet and probably take them all as it may be contagious or it may be coming form the dam and if so, something like that can cause you to lose them ALL. Was she examined after having the pups. Standard protocol is within 24 hours.

Blood in the stool can be caused by a number of different things including worms, infection with bacteria or viruses, or trauma.  There are many other causes which are much less likely in such a young dog.  I would recommend contacting your vet before the condition worsens.  If your pup is showing signs of illness like diarrhoea, lethargy, depression or a lack of appetite you should seek veterinary care immediately.  Puppies do not have much reserve and their immune systems are not properly developed so they rapidly succumb to problems like this.