Thank you for the additional information.
One of the most common reasons for loose stool with blood in puppies is parasites. . Not just worms but also microscopic protozoa such as coccidia and giardia Click here
If he actually passed worms with the last treatment then he should be re treated again. The reason I say this is because deworming only kills adult worms leaving the immature ones to develop. Also if this is due to coccidia or giardia the deworming will not help.
Overgrowth of bacteria can also cause this problem.
I would suggest asking your vet to take a stool sample and send it out to the lab. Lab testing is much more accurate and will test for worms, protozoa and bacteria.
Food changes can also cause this problem, however it is normally self limiting lasting only a few days until they adjust. Some dogs can have sensitivities to certain proteins such as chicken, beef, lamb or things like corn so that is also possible.
Because he has not had all of his jabs we also have to consider the parvo virus but with this they normally have vomiting and loss of appetite as well so that is not to high on my list of concerns.
I would start with having the stool tested. If that is clear then I would try changing the protein source in the food.
I hope this helps. Please reply back if you have additional questions or concerns and I will be happy to continue.