Why is there a “do not file” water mark on the city tax portion of my taxes? Can I fix it or send it as is?

No, it isn't ready to be filed if it has the watermark.   Have you been through the filing steps yet and paid any fees?   Either the form has not been finalized by the city yet (unlikely for a city return) or you have not gone through all of the filing steps yet.   What city and state are you filing a return for?   And have you already e-filed your federal and state returns?  

Yes, I filed in January and both federal/state were accepted. I mail the city form. Jackson MI.

If you filed in January the city return may not have been ready for filing.  This would have caused the do not file watermark to appear.  If you already mailed the return, you can contact the city to verify if the return was processed.