Can a toothache cause death?

Not exactly: A toothache is essentially just a description for tooth related pain. What you may be referring to are the rare stories where a tooth infection causes death. In these cases it is generally a severe abscess of an infected tooth, resulting in swelling and a spreading of the infection to the body. This is rare, but still a risk. Another serious risk is swelling that can occlude your airway.

No, but...: An ache cannot cause death, however tooth infection can. I have seen a brain abscess form tooth infection that was fatal. Before antibiotics people died of tooth infection all the time. Today with modern dental techniques tooth problems can be treated effectively and comfortably.

Probably not: We know from anatomy that an untreated tooth infection in the upper back teeth can drain to the cavernous sinus and cause a brain infection which would lead to death if left untreated. Modern antibiotics have pretty much eliminated such occurrences. However new strains of bacteria pop up all the time and some are showing resistance to antibiotics. If you have pain, have it looked at.

Rarely: Infected tooth can possible travel to the brain via cavernous sinus leading to death.

Toothache? no: No one dies from a toothache. It can be excruciating painful in some cases but will not cause death. If you meant to ask can a problem with a tooth cause death, then the answer is: relatively rare but possible. If a tooth becomes infected from any number of reasons, the infection can spread to other parts of the body and cause serious complications, including in rare instances death.