Removing old countertops

We are getting new quartz counter tops. We are going to reuse the existing cabnetry. To save a few bucks, we said we'd remove the old tops. My husband tried to remove the island top but couldn't without damaging the cadnetry. We are concerned that when we try to remove the old counter tops (they appear to be adhered the same way-lots of glue and corner blocks) we'll end up damaging the cabinets below. Any tips on taking off old counter tops safely, doing the least bit of damage to the cabinets below?

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