How do you soften the glue on those blown glass ornaments on a mirror?

Try heating with a blow dryer. Depends on what glue was used, maybe nail polish remover, but make sure it doesn't run to the backside of the mirror as it will remove the backing

I would try the blow dryer first, start on low heat and work your way up the heat settings if you have to. That would probably be the least damaging way to start trying to remove blown glass ornaments which can be a bit fragile some times.

I removed some two sided commercial tape with dental floss, used like a garrote. If you can get the ornaments off, you can use a razor blade to scrape off the residual glue.