Voy a terminar contigo
Is this "I am going to finish with you" as in "I am going to break up with you"? Gracias.
That would depend on who's saying it to whom, under what circumstances.
A very angry woman furious at having discovered her boyfriend cheating on her in her own house, saying that to the aforementioned boyfriend with a large butcher knife in her hand, probably means it both ways.
Obviously there are many ways to say this. One way to show total and complete separation is to revert back to Usted form, ie: ¡Ya estuvo bueno con usted! "¡Váyase por su propio camino y me voy por el mio!"
Yes, your translation is correct
I don't want to go out anymore. No quiero salir más contigo.
I want to break up with you. Quiero que terminemos.
I want to break up with you. (stronger) Quiero romper contigo.