Learn Portuguese (Portugal): Tu não discutiste a mensagem comigo.

Discutiste comes from the regular '-ir' verb discutir. To make the tu (informal "you") form in the simple past, you drop the '-ir' ending and add -iste. So, discutir becomes discutiste.

I've heard that discutir can mean "to argue". Does it mean "argue" or "discuss" here?

It can mean both! Discutir is often used for having an argument, but it also simply means "to discuss" something. In this sentence, "discuss" is the most natural translation for talking about a message, but depending on the context, it could also mean you didn't argue about it.

Why is "with me" translated as one word, comigo?

In Portuguese, when you combine the word com (with) and the pronoun for "me", they merge into a single special word: comigo. You will never see com mim; you must always use comigo.

Why does não come before the verb instead of after it?

In Portuguese, the negative word não always goes directly in front of the verb it negates. So it must be não discutiste. The subject tu is optional, but when it is used, it goes before the não.