In the words of Raymond Carver,
Tone is a very hard thing to talk about objectively, but I feel that a writer's tone is his signature, not just the way he crafts his stories. I can tell you what my tone isn't. It's never satirical. And it isn't ironic, clever, or glitzy. The tone is serious, by and large, though obviously some of the stories are humorous in places. I don't think a tone is just cobbled up by a writer. It's the way the writer looks at the world, and he brings his view to bear on the work at hand. And it can't help but infuse nearly every line he writes. (Source.)
Did you notice that Carver talks a lot about what his tone is not? He isn't trying to be tricky or pull any punches. He isn't trying to get fancy or come up with complicated plot twist. That tells us that when he looks at the world, he sees it for what it is, and then writes it. So what world is he seeing in "What We Talk About When We Talk About Love"?
Carver also tells us that his "stories often have to do with loss, and as a result the tone is, well, not somber, but severe. Grave, maybe, and somewhat dark […]." And why wouldn't he think that? As he puts it, "Life is a serious business, isn't it? It's grave, life is, tempered with humor" (source).
Carver was trying to echo the tone of life, as he saw and experienced it, in his stories, and this one is no exception. Considering how much violence is packed into it (beating, stalking, rat poison-drinking, highway crashes, and more), we'd say, yes, the tone is serious and even grave.
But let's take a closer look. Take, for example, this scene between Mel and Terri:
"Honey, I love you," Mel said.
He leaned across the table. Terri met him halfway. They kissed. (73)
This is a loving moment, right? Then why so serious? Mel's words are loving, but the description of his actions is blunt, to the point, and unadorned. That description takes this loving moment and turns it into something serious, somber, and grave.