Learn French: Vous ne refusez pas l'accord ? Si, je le refuse. - You aren't refusing the agreement? Yes, I am refusing it.

Because the question is negative (Vous ne refusez pas...). In French, whenever you contradict a negative question or statement to say "Yes, actually I am" or "Yes, I do," you must use si. If you used oui, it would sound like you were agreeing with their negative statement.

What does the le represent in je le refuse?

It is a direct object pronoun meaning "it", replacing l'accord (the agreement). Even though we only see l' in the first sentence, accord is a masculine noun, so we must use le to refer back to it.

Why is the pronoun placed before the verb in je le refuse?

In French, direct object pronouns like le, la, and les always go immediately before the conjugated verb, unlike in English where we put them after the verb. So "I refuse it" becomes je le refuse.

Could I just say Si, je refuse and leave out the le?

It is much better to include it. Unlike English where you can sometimes just say "I refuse," French prefers you to include the object pronoun so the thought is complete. You need the le to explicitly say "I refuse it."