I started to put down batts insulation in the attic space above garage and noticed that the wiring coming from one of the outlets was stripped a little too much and one of the leads of the romex is actually exposed outside of the electrical box. I'd like to correct this before putting insulation near the outlet. The outlet is from the ceiling of the garage so it's actually between the joists in the attic space where the insulation was being laid. Can I just wrap the exposed portion using electrical tape or should I cut the exposed area so that none of it extends outside the box? I'd rather not redo the entire cable if possible.

Wrapping it with a several layers of electrical tape will be fine.

The is probably a clamp in the box that is supposed to hold the Romex. It may have just slipped out. Kill the power first. Look for a small set screw right where the romex enters the box. It will be outside the box. Loosen the screw, push the Romex in further and retighten the screw.