I am a landlord and legal resident of South Carolina (an area that is a suburb of Charlotte NC). I rented my SC property to a woman who will soon be evicted because she owes me $3,500+ in back rent. I have filed eviction papers and I want to know if I'll be able to sue to garnish her wages. My state does not allow wage garnishment, but my tenant is not (and has never been) a legal resident of South Carolina. She works in North Carolina and files taxes as a resident of either North Carolina or Connecticut. She's moved around a lot and she's a big scammer, so I'm not sure if she even pays taxes in any state.

Since she is not SC resident, can I sue her to garnish wages?

You need to get a lawyer. A garnishment is a suit against a third party that owes money to your tenant, such as an employer or bank. The garnishment does not depend on where the tenant resides.