The title points to the Purple Heart, the medal given to wounded soldiers, and the poem seems to circle around what a war does to the person who comes back. The opening line is the strangest and most striking: the war ended "some other me." It reads as though the speaker who fought is no longer the speaker who is writing, as if the war finished off a former self rather than simply finishing.
The next lines move toward closeness. "We were as one / in the assignment of heart" suggests a shared bond, perhaps among fellow soldiers, perhaps between the old self and the new one, and the pun on "heart" echoes the medal. The ending is quiet and a little haunting. Having "seen the way to write / letters home" implies that some kind of clarity arrived, yet it sounds more like learning a task than feeling relief. The mood is detached, hushed, and tinged with grief, with emotion held at arm's length.