Mice don't care about insulation. They will build nests in it and drag it anywhere they want. I've had mounds of it behind cabinets against the wall at the floor level.
BTW - you don't want to fill the area in your illustration with insulation. Your roof needs to 'breath' and the vents in your soffits allow air to move up the inside of your roof and remove heat and moisture.
Blocking this area off with insulation will cause mold and rot to the inside of your roof structure.
They make 'baffles' that go into that area and attach to the underside of the roof. The insulation goes 'below' the baffles and across the ceiling joists - not the underside of the roof itself. The baffles allow the movement of the air.
If it was me, I'd do a plywood floor in the attic over the insulation with a drop down ladder for extra storage. Then sheath the ceiling with plywood or similar material.
Sheetrock is inexpensive and easy to paint - but it can crack along the taped seams in a garage as they have a tendency to move around in the wind more so than a house.
Later . . .