Question how much is cut off? Off to the elbow or shoulder? Off to the knee or hip? Off to the...?
Also is the way I lose them heroic or badass?
Both legs and one of my hands. I'm not sure which. My right is dominant, but it has some movement issues and is more likely to have problems in old age, but again I use it for most things. So probably off with the left.
I live in a 1st world country and my family is moderately well off, so aweseome spring legs and rehabilitation to use them is definitely possible. Likewise if it's only to the elbow I can get a fake hand with modular joints/interchangeable with with hook/knifeblade. I'd probably be depressed initially, but I'd try to eventually move on with life and never let my injuries slow me down.
Also another option for your question could be left and right eyes.