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Does Giant Killer get destroyed with Warstorm Surge? or is it able to destroy my creature with it’s instant ability?

My friend has Giant Killer out on his battlefield. I have Warstorm Surge and I bring out Gisela,Blade of Goldnight. Does Giant Killer get destroyed first as a creature before my friend can cast it’s instant adventure? Or is he able to cast its ability to destroy Gisela and exile itself before being destroyed?