When infection enters the body and is carried through the body in the blood, it is the effect it has on the internal organs that kills the person.
For example, infection in the blood can cause increase in sticky platelets in the blood, which increases the likelihood of a clot that can move to the lungs or the brain, and cause death.
Infection in the blood can also affect the functioning of the kidneys causing mild to acute kidney failure, also a potential life threatening situation.