Insulating exterior wall during partial renovation?
 

I'm going to remove tile & mortar bed from the lower half of an exterior wall in one of my bathrooms, and replace it with drywall. I plan to put fiberglass insulation where I can in the studs.

My question is, should I put up a vapor barrier too (I live in N GA), or there's no point unless I'm putting up a vapor barrier over the entire wall?

I would hope you're not going to replace with drywall and then tile over it. Use a tile backer board and waterproof it. Then install the tile. That will take care of your vapor retarder issue. It will be built in as part of the tile/waterproofing system.

I'm removing existing tile, mortar bed and metal lathe from the wall. Drywall will be the finish surface.

Then I would use a vapor retarder over the insulation and if it's in a bath, I would use a mold resistant drywall like Densarmor,