I live in NY but my company is in NJ. Which wages should I remove when doing the state taxes?

The income earned while in New Jersey (NJ) is taxable to NJ as a nonresident.  File the NJ return first so that TurboTax knows the income and tax, then it will be carried to the New York (NY) return for your credit.  NY will give you a credit for taxes paid to NJ on the same income.  

You are not required to include your IRA distribution on the NJ tax return, only NY. When you step through the NJ return, there will be a screen where you can change the NJ amount for your IRA distribution.  Make sure you do not have NJ in any state filed in the 1099-R entry.  See the image below.

The credit for taxes paid to another state on the same income is used on your resident state because they do not want you to pay taxes twice on the same income.  As the resident state all worldwide income must be included.

The credit for tax paid to another state on the same income will be the lesser of:

1. the tax liability actually charged by the nonresident state, OR
2. the tax liability that would have been charged by your resident state