It can't be changed. Money you earn by working in AZ is taxable by AZ, regardless of whether or not you are an AZ resident.
You must file two state returns: a non-resident AZ return AND your normal home state NM return.
You'll be able to take a credit on your NM return for the taxes you pay to AZ, so you won't be double-taxed.
In TurboTax, be sure to complete the non-resident state return first, before you do your home state return, so that the credit flows properly.
**Answers are correct to the best of my ability but do not constitute tax or legal advice.