Three short lines, and a whole small comedy sits inside them. The speaker tells their dog to relax, and the humor comes from how ordinary and how hopeless that is. A dog can't follow the instruction. It doesn't understand the word, and it's probably too excited, anxious, or wound up to settle just because someone asked.
The poem is also a little gentler than a simple joke. The speaker seems patient, maybe a bit amused, maybe a bit tired. There's a hint that the speaker might need the advice as much as the dog does. Anyone who has said "calm down" to someone who couldn't, or to themselves, will recognize the feeling.
The mood is light, dry, and affectionate. The short lines and the stretch of white space after "relax" create a pause, as if the speaker is waiting to see whether anything happens. Judging by the text alone, probably nothing does, and that's what makes it funny and warm.