if you say that something will happen over your dead body, you mean that you will do everything you can to prevent it 'Josh says he's going to buy a motorbike.' 'Over my dead body!'If they cut down those trees, they'll do it over my dead body.
In no way, under no circumstances, as in Over my dead body will you drop out of high school. This hyperbolic expression is often used jokingly. [Early 1800s]