Welcome, Slupa!
It doesn't look like it is dying at all to me. Everyone of those gray canes has green growth coming off of it. As roses mature their canes do turn gray or brown like bark. That does not mean they are dead. Only remove any canes that do not have any green growth coming off of them.
Does this rose rebloom all summer? If so removing the spent blooms will help it to bloom quicker. It also keeps it looking neater. Just keep it watered and give it a little fertilizer for now and wait and see what it does.
By the way, knowing where you live and what zone you are really helps us with giving advice on how to care for a rose.