Three short lines, and the whole poem hangs on one word: "murdered." People usually say they "killed" or "squashed" a spider, if they mention it at all. Murder is a heavy word, one we save for people, and using it here makes a tiny, everyday act suddenly feel serious.
The speaker seems to feel guilt, or at least unease. Judging by the word choice, they can't shrug it off as nothing. There may also be a hint of dark humor, a wry exaggeration, as if the speaker is half aware of how dramatic it sounds. The poem doesn't settle which, and that ambiguity is part of its charm.
The mood is quiet and stark. The short lines and the lonely "today" at the end leave a pause, like a held breath. The poem makes us wonder how much a small life counts for, and why we so rarely stop to ask.