Both sentences are not correct. The problem you have is called dangling modifier problem. The phrase "severely injured" is hanging at the end of the sentence without being clearly attached to the subject. Grammatically , it looks like "the hospital" is "severely injured" instead of the subject "HE". This structure makes it sound ambiguous or awkward. It would be better to say the following: Severely injured, he was taken to the hospital.

Both sentences are not correct. The problem you have is called dangling modifier problem. The phrase "severely injured" is hanging at the end of the sentence without