In Minnesota my 15 year old son no longer lives with his mother and never will. He now lives in a REM faucility. Do I need to continue to pay child support to his mother?

Generally yes, you do. Until the court says otherwise. So, head to your attorney and file a Motion for a change in support. You may then both be held financially accountable for your son's care at REM. Also, child support may continue to be paid to his mother especially if she is providing for his clothing, extras, any payments for the REM services, health or dental care, etc. Whether he is living under her roof or not, may not be the best indicator.

Do you have partial legal custody of the child ? You should have been notified as to what's taking place. Your ex may have given up guardianship to make your child a ward of the state. If that's the case then you need to go back to court and see where the child support goes. It may be applied to the state for his cost and care.