Ice dam overflow channel.

Cutting an overflow channel in the ice dam.
This must be done with great care and by an experienced roofer. A small sharp ax in the hands of an amatuer will quickly cut through ice, roof slate, sheet metal and guttering. Only cut enough ice to relieve the majority of the ice dam and get some of the water flowing off the roof.
Then spead some ice melter granules on the channel and around the ice dam to help melt off the ice.