Donne doesn't beat around the bush here. He tells us right away what's up. This is a valediction. That's not really a technical distinction for a rigid form of poetry, but plenty of valedictory poems are out there. Surely you know that a valedictory speech is delivered on graduation day. A valediction literally means "to say farewell."
The second half of the title is a little bit more interesting. It feels more Donne-y. Donne-ish? We would expect that a goodbye poem would paint a beautiful sunset for us with the lovers kissing through their sobs. We would think a poet would encourage that sort of thing. Instead: no soup for wifey. Donne clues her (and his readers) into his deliberate efforts to go against the traditional goodbye. So, when we set our expectations from the title, we are more readily able to see the cleverness at play in the poem.