NOt just glue, large clumps of glue that were holding up mirrors. I took the mirrors down and now have patches of glue that need to be removed before painting. I would like to remove them without damaging the drywall too much. So far scraping them and using a box cutter has not worked!

Scrap it off and patch the spots. I doubt you can get it off without some damage to the drywall.

WHat kind of glue? Will a heat gun work? Temporarily try a hair dryer.

I can always give my new EXPENSIVE tool a plug. Cheapest new version $200. Blade $28
Give me a PM if you want to know what it is. It has lots of uses.

No matter what you use you will need to float a thin coat of joint compound on the surface before you prime and paint. The glue is likely stronger than the paper surface so forget thinking you might get it to peel off. Take a 4 or 6" tapers knife and just slide it flat with the drywall surface and slice it off, hit the knifle handle with a mallet or hammer if you want.

Ballenger right, its easier to repair than to mess around with it. Come back if you need guidance patching.