If I currently on probation for a gross misdemeanour DUI and I'm in state DUI court, if I leave will I be extradited back?

It?s impossible to know. When you miss a court date in Minnesota, the judge will issue a warrant. The warrant can be state only or nationwide. If it's a nationwide warrant, and then you are arrested out of state, then the Minnesota prosecutor will need to decide whether to extradite you back. So, the best answer I can give you is that there's definitely a chance that you would be extradited.