Did you get this from the Angry Birds movie? Then it's exactly as Phil described. However, the speaker is a bird, and the verb "pluck" goes with "feather"... so it's a play on words. It's not standard English. Just a joke for this one particular movie.

I've never heard of it. I think it may be a 'polite' form of the saying 'fuck my life', which people online abbreviate (shorten) to FML. This is used when something bad has happened to someone. Car broken down? Fuck my life! Pizza burnt my mouth? Fuck my life! etc. 'Pluck' my life could be the same as how we sometimes say things like 'Fudge!' instead of 'Fuck!' or 'Fiddle sticks!' instead of 'Shit!'.