Translation:I already finished my homework.
しまう for finished? I don't believe it's used very often that way outside of using it after the て form of a verb. I would say it's more common to hear おわった, した, or やった to express the completion of a noun based off of what I've heard and seen... but I could possibly be way off too.
Grammatically, やる ("to do something ") is transitive, so the subject would be the person/thing doing the action and the object would be the thing being done.
"As for homework, (I) did (it) already."
In contrast, you could use an intransitive verb, like 終わる (to finish), which does not require a direct object. In this case, the subject is the thing that has been finished. There is no direct object and no actor is involved in the action. No one finished the homework, the homework is simply in a state of already being finished.
"As for the homework, (it) is finished."
Subjects and objects can be dropped from the sentence in Japanese, but the verb tells you a lot about what is happening, even in their absence. Just because the subject is missing, that doesn't mean it has ceased to exist. An implied subject is still grammatically significant. As you get deeper into the language it will be increasingly important to understand not just what is being said, but what is being left unsaid (and why). Also, you will want to keep an eye out for transitive and intransitive verbs and verb pairs. They are a very significant part of basic Japanese grammar since the way you use particles will be different with a transitive verb compared with an intransitive verb.
Here is a brief guide to get you started: