phrasal
or throw up the sponge or throw in the towel
Etymology: fr. the practice of a boxer's second of throwing a sponge or towel into the ring for his fighter to wipe his face, this being taken as an admission that they were no longer willing to continue the bout
: to abandon the struggle : acknowledge defeat : give up
throwing in the sponge and failing to accomplish our mission — Glen Jacobsen
when so many had thrown up the sponge and surrendered all faith in humanity — Van Wyck Brooks
when the chaplain throws in the towel over your problem — All Hands