In her poem "Liberty and Peace" Phillis Wheatley refers to the often brutal and bloody conflict of the Revolutionary War between the American colonists and the British. The war was fraternal in that it set men against their brothers. Not all Americans supported the rebellion by any means; some chose to stand with the British. Entire families were split right down the middle, mirroring the savage conflict rapidly developing on the field of battle.
But the Americans and the British were also brothers, linked together by common ties of blood and heritage. And yet despite these close bonds they fought each other in battle, "on hostile fields." This is what Wheatley is referring to when she talks of "fraternal arms." And "Mutual deaths" means that, in this terrible war, there were deaths on both sides. And what caused such deaths was the "mutual rage," the burning anger and animosity that existed between the Americans and the British, men who were supposed to be brothers.