Can file my tax without paying Michigan State tax as Active-duty military on PCS orders?

Yes, as an active-duty military member on PCS (Permanent Change of Station) orders, Active duty military pay is exempt from Michigan individual income tax. However, most interest, dividends, capital gains, and other income received is subject to Michigan individual income tax

For more detailed information, you can refer to the Michigan Department of Treasury's page on Tax Information for Military Personnel.

@djbvjel 

And in the My Info section, be sure you do NOT indicate you are a resident of MI, nor do you indicate you moved to MI from some other state.  You remain a resident of your HOR state no matter where you are posted to with your PCS orders.   

........(or remain a resident of your State of legal residence ((SLR)) if you changed it to a different state at some time in the past, by filing a DD2058 )