Which state were you convicted in? In addition to your DUI, why is it you broke the law by not getting a MN license in a timely fashion (you have 60 days)? Were you also cited for that?
Anyhow, if you were convicted in TN, you're going to have to square yourself with TN, before you can get a MN license.
If you were convicted in MN, you're going to have to square yourself with them first (as they almost certainly suspended your driving privileges there). If TN also suspended you as a result, you'll have to square yourself with TN. Only after being in good standing with both states can you get a MN license.