Here is what Masterplots says about Mithridates:

The tale of Mithridates with which Housman closes the poem serves as a parable. The poisons consumed by Mithridates fortify him against catastrophe. He survives where others would perish, exactly as the reader will survive the awaiting catastrophes of life having taken an antidote in the form of Terence’s painful verse, which may produce “belly-ache” but will “do good to heart and head/ When your soul is in my soul’s stead.”

That, then, is not only the purpose of Housman’s verse but also the essence of literature itself: to prepare one for the inevitable sorrows of human existence, to face tragedy with dignity, to prevail against the “slings and arrows of outrageous fortune” as long as one is sustained by the breath of life.

I think you need to read the last line with a hint of sarcasm. They put poison in his food and drink, but none of it harmed it. Indeed, it was only themselves that they hurt. So, as Housman says, "Mithridates, he died old." That is, he died of old age rather than at the hands of others.