I'll be hanged if I (do something)
I am determined not to do something. I'll be hanged if I let some young upstart like you take control of my company!
I'll be hanged
1. I am very surprised, as in, Well, I'll be hanged; there's Susan.
2. I'll be hanged if I. Under no circumstances will I, as in I'll be hanged if I let you do that. Both of these hyperbolic colloquial usages allude to being executed by hanging.