My first thoughts were to reconsider if removing the braze ons is really in your best long term interest. We get a new toy and have all kinds of new dreams about how we're going to use it. Then time, changes in our lives and the very real possibility of another new toy entering our stable (and juggling the bike's marching orders) happens. I don't know how many times I've wished I either had left on or had added to begin with braze ons after the frame was painted, often a bike later

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If one must remove braze ons I strongly agree with Eric. A hack saw and file. will do FAR less damage then a die grinder. If one has to ask about this one doesn't have the experience to handle said grinder in a manor that prevents damage possibility. I resort to heat rarely but do use it sometimes. No matter what I use I will have to file and sand the, now, razed spot. Often there will remain a visual evidence of where the bit had been located, a slight depression (especially if brass was used) and or ripple to reflections. Of course if powder coating is to be done this will help hide that. Rarely I have had to drop a spot of silver onto where the braze on had been to fill what was the resulting surface after removal.
Here's a shot of a drop out being pulled with a vice grip as the weight. Note the tether to control where the hot drop out falls to (as in away from my OA hoses).
Also here's a link to a Flicker album with my tandem having many braze ons removed and installed with some text for each shot.
https://www.flickr.com/photos/731955...57676883117315 Andy.