Praise be to Allah.
Driving too fast is not a good thing, because of the accidents and dangers that result from it. Hence the scholars have spoken sternly about it and they regard driving over the speed limit as carelessness on the part of the driver, so he is liable for loss of life, limb or property that results from that. Any death that results from that is regarded as accidental killing or manslaughter, for which he must pay the blood money (diyah) and offer expiation (kafaarah).
Shaykh Ibn ‘Uthaymeen (may Allah have mercy on him) was asked: A person died because of an accident in which the car was speeding. Can it be said that this is a kind of suicide?
He replied: No, this is not suicide, rather he has killed himself by mistake. If speed was the cause of the accident then he killed himself by mistake, because if he were asked: were you driving so fast to die? He would say: No. So this is not suicide. But it may be said that he killed himself by mistake. End quote from Liqa’ al-Baab il-Maftooh (73/19).
Taking the wounded and injured to hospital is a good deed, for which a person will be rewarded. But he should not bring harm upon himself or upon the injured person by driving too fast or going through red lights. That may lead to something that will cause a delay in bringing the sick person to the hospital.
As for the one who died as the result of this speeding, we ask Allah to forgive him, and to reward him for his good intention, and that is not regarded as suicide, because he did not mean to kill himself, rather his intention was to do good by taking the sick person to hospital quickly.
And Allah knows best.