At one point in “Three Billboards Outside Ebbing, Missouri,” Frances McDormand tears the movie open, showing you what a broken heart looks like. It happens during an uneasily intimate encounter between her character, a tough number named Mildred, and an ailing police chief, Willoughby (Woody Harrelson). Until then, Mildred has seemed impervious to his pain. She has rented three billboards attacking his failure to solve her daughter’s murder — one reads “Raped While Dying” — and has been so wrapped up in her hurt that she hasn’t seen anyone else’s. When she realizes how sick Willoughby is, she looks at him as if for the first time. She’s staggered, and so are you.

The pain of others haunts “Three Billboards,” at least whenever the writer-director Martin McDonagh lets it. A playwright (“The Pillowman”) turned filmmaker (“In Bruges”) who’s somewhat of a subgenre unto himself, Mr. McDonagh is a pain artist whose tools include absurd violence, cruel laughs and sucker punches. He skated through his last movie, “Seven Psychopaths,” a barely there comedy that pivots on a creatively stalled screenwriter. As this précis suggests, Mr. McDonagh doesn’t have much to say in that movie — it has a bunny, stolen dogs, guys with guns, good and bad jokes — but what little is said is said by very fine performers grooving on all his words and larky nonsense.