Despídase is a formal command meaning "Say goodbye". It comes from the reflexive verb despedirse, which refers to the act of bidding farewell.
In the song, the singer makes a painful request: "si... fue la despedida, 'tonces venga y despídase bien" (if that was the goodbye, then come and say goodbye properly). Using the formal despídase (instead of the informal despídete) adds a layer of emotional distance and gravity to this desperate plea for closure.
This song is a messy, honest look at a breakup from someone who knows they messed up. Carin Leon isn't trying to be the good guy here. He admits he had to leave a letter for his ex because she blocked him: "Perdona por ser como soy, es que no me desbloqueabas" (Sorry for being who I am, you hadn't unblocked me). He knows the relationship is over for her, but for him, "aún no acaba" (it's not over yet).
He seems to think he's broken when it comes to love, wishing he could love her but admitting, "es que no lo sé hacer" (I just don't know how to do it). He even hopes that "Quizás en otra vida tenga un cora' que sirva" (Maybe in another life I'll have a heart that works). Since this might be the final goodbye, he asks for one last proper one: "'Tonces venga y despídase bien" (So come and say goodbye properly). It's a blunt, self-aware song about repeating the same mistakes and wanting one last moment before it's truly over.