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I chop mine back ruthlessly, which freshens it up and also limits its spread somewhat. Mine, however, is the common or garden red/orange variety.
I'd chop it all back now, before it begins to grow again.
If you garden in a sheltered spot and it's already thrusting out new spring leaves then just take out the dead stuff.
You won't kill it either way.
I would cut off the brown dead/dying leaves.