Frosty garden ( how to kill a rhododendron?)

It was  still very cold by the time we got back from a 60th birthday party and garden jobs beckoned. The extra shows a  rhododendron bush that is blocking our view . Our neighbour owns half of so we cant get it removed altogether  but I would like our half  (the RHS) to go completely. Its horrid stuff-.  as soon as you prune it it grows again more vigorously.  I am hoping if we cut  it now the frost will get into the roots and kill it. Any other suggestions?