The structure here is Topic, Subject, Verb, just like it has been the entire course. The only difference is that the topic is a little more complicated than usual.
청소 is being described (in a sense) by 네 방, and then the topic marking particle is added at the end of that full description.
네 - you/your
방 - room
청소는 - cleaning (the noun form of 청소하다 with the topic particle 는 added to it)
네가 - you/your (with subject marker 가)
해 - to do (present informal tense)
Together, the literal translation is:
Your room cleaning you do!
Or more naturally
You do your room cleaning!
If we translate more naturally than that, since it is clearly an imperative sentence because of the exclamation at the end, you get:
Clean your room yourself!
I'm having trouble parsing the grammatical relationship between 네 방 and 청소. Is 방 and 청소 acting as a singular compound noun? If they aren't a compound word here, are there some unmarked particles inside of the topic phrase that someone more fluent would interpret in the underlying form?