If West Virginia is your Home of Record, your active duty military pay while serving outside of WV is exempt from state taxes.
To claim the West Virginia exemption, you will file as a non-resident. As you begin your WV return, look for the page titled "We've Recommended a Residency Status". Indicate that you want to change your residency. On the following page select "Special Nonresident (Form IT-140NRS)". This will exempt your WV military income from state tax.
On the Tell Us Your State of Residence screen choose Out of State in the drop down box the right of State of Residence.
See screen shot below.
Note: Ensure your W-2 is coded as active duty military. Once you click Continue after entering your W-2 in to TurboTax you will see the Do any of these uncommon situations apply to this W-2?. Click box next to Active duty military. See Screen Shot below.