What species is this?
A pine?
A maple?
A ficus?
... ?
It's as if you woke up on a hospital bed and a surgeon would ask you:
"What would you like me to remove ? An eye, your legs, or both your balls?"
"Dead wood" is only convincing on species that have this feature in nature.
Talking about things you don't name is, er...
Well your English is much better than mine, and so must be your sense of humour, so you will probably find the right term