It is illegal to drive without a side mirror in Michigan.
Michigan law states that a person shall not drive a vehicle if the drivers visibility through the rear window is obstructed, unless the vehicle is quipped with 2 rear view mirrors or side mirrors which is 1 one each side and they must be adjusted so that the driver has a clear view of the highway or road behind the vehicle.
Michigan law Sec. 708. IIRC you need two rear view mirrors and one has too be the drivers side door mirror.
There are a few states that require both side mirrors to be present and functional, but in most states, it is considered legal to drive with just one side mirror when it is complemented by a second one—like your rear view mirror.
It is not illegal to drive with a single broken mirror, although you do need to be careful.
The mirror needs to be secure to the vehicle so that it doesn't fall off.
You also want to make sure that the glass is stable enough so you won't be leaving broken glass all over the place.