"My paycheck will be deducted by full state tax for VA state and some minimum state tax for NC state.
Is this correct !!"
If you're a resident of VA and you never physically work from a location within NC, then NO, it's not correct. As @rjs explained in his original answer to your question, the work income of a VA resident who never physically works in NC is not subject to NC income tax. Hence your payroll office should not be withholding NC taxes at all.
Your "work location" is where you actually (physically) perform your work.
As @NCperson stated, if you can't get your payroll department to correct your withholding, then you can resolve the problem at tax time. To do so, you'll have to file a non-resident NC tax return on which you claim zero NC income. This should result in NC refunding to you all the incorrectly withheld NC taxes.
**Answers are correct to the best of my ability but do not constitute tax or legal advice.
