There were many ways to die in ancient Greece but ox-cart related deaths were a rarity ... to the best of my considerable knowledge, there are no fatal ox-cart incidents on record ... if you want to talk about chariots, then we have quite a few fatalities ... probably one of the most dangerous places you could be during a battle was in a chariot ... driving an ox-cart was a low-fatality sort of occupation if you didn’t provoke the ox and stayed in the cart.
Homer was not killed by an ox-cart ... not only would it have been an un-poetic death, it would have been downright embarrassing.
Quit embarrassing yourself and get back to the Quiz!