Las mujeres sí van.
Duolingo translates this to: The women will go. The women are going.
I haven't seen "sí" used in this way. Is this common?
Yes, this is a pretty common construction, at least in spoken Spanish. When you add the "sí" for emphasis before the verb like that it emphasizes the affirmative nature of the verb action, usually in contrast to a negative statement. Sometimes you can translate it like the "do" that you put before a verb to emphasize it.
For example, Los hombres no van a comprar, pero las mujeres sí van. The men aren't going shopping, but the women ARE going (even though the men aren't).
No quiero que vengas. Lo que sí quiero es que me digas la verdad. I don't want you to come. What I DO want is for you to tell me the truth.
Hope that helps.
Is this construction ever used in a context in which emphasis on the "affirmative nature" is not important?