Just to add my personal anecdote to illustrate that this can easily be done.
I was a graduate student at Ann Arbor, Michigan. My stipend (or rather pay) came to less than $2,000 a month after taxes (during the 8 months of the school year). The pay package fortunately covered any tuition expenses and also health insurance - I think though that this is pretty standard anywhere in the US.
I was nonetheless able to save well over $1,000 per month, even without making any effort to do so.
My monthly expenses were usually just $500 for rent (plus all utilities, including internet) and another $200+ for food. I always had my own private room. Food was mostly just groceries, with occasional eating out. Anything else I treated as a luxury. For example for transport, I simply had a bike (≈ $130 off Amazon) and for my cellphone I just had a prepaid one (you can pay $100 for a cellphone that has something like 1000 minutes, 1000 texts loaded - this can easily last you a year if you're careful). The cost of living in Ann Arbor is probably slightly higher than the US average, though certainly lower than NYC or SF.
So I'd say yes, saving $400 per month is easily doable, if you're prepared to live a lifestyle that is considerably more frugal than what the typical American is accustomed to. And it sounds like you are indeed prepared to do so.
Note that legally speaking, if you're a dirty foreigner (like I was), you're legally allowed to work only 20 hours a week during the school year. So if you're already a TA or RA, it's likely that you cannot legally work any more hours. However you can still find freelance and lucrative work, e.g. tutoring undergraduate students. This is technically illegal but it's unlikely you'll ever get caught (many foreign grad students work off-the-books but I've never heard of anyone getting caught).