Let the gum harden naturally, then harden it up a little more with an ice pack (if they were your Chuck Taylor's, I'd say toss them into the freezer for an hour or so).
Then, take a knife and work carefully, but not necessarily delicately, beginning on the sole. You may need a little edge dressing when you are done.
If you don't get 100% off the bottom, walk around the block and that'll take care of most of the rest.
They are lovely but they are cord boots with JR soles. I wouldn't worry too much about the soles.