In formal logic a tautology is "a propositional formula that is true under any possible Boolean valuation of its propositional variables".
The proposition "he became dead by means of making himself dead" contains the propositional variable "by means of <item>", and there is no valid value for this variable which would make the propositional formula evaluate to false.
Thus in formal logic the proposition "he became dead by means of making himself dead" would indeed be a tautology.
I don't think one is allowed to trim the proposition like that. It doesn't say "he became dead by one means or another", it states quite unequivocally that his death was a suicide, and this statement can indeed be false under various circumstances (e.g. if he had been murdered, or fell off a ladder, or just miraculously died for no apparent reason).