How to remove countertop from cabinets while sacrificing it to maximize the chance to reuse cabinets

countertopsdemolition

I have a row of "base" cabinets in the living room that I'd like to remove, but I would like to use several of them elsewhere.
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I don't care about the top (which is some kind of stone and already crumbling pretty badly both here and in the kitchen), but I'm not sure how to remove it without destroying the tops of the cabinet boxes.

I can tell that there is some sort of shiny white material that was used to "glue" the top to the cabinets in several places, here's a picture:
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I can slide a blade in there, but haven't had any success either chipping any of it away, nor "scoring" it in order to be able to lift it off. I was able to separate the back of the countertop from the wall pretty easily, so this white goo is all that "stands" between being able to use cabinets elsewhere. Is there anything I can try short of cutting countertop into pieces a little at a time? And if that's the way to go any suggestions for tools to use?

Here is a picture of the countertop near a seam where it's crumbling the most:
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Best Answer

Since you do not care to preserve the top you could break it apart into smaller pieces. Breaking it that can typically be done with a sharp whacks with a heavy hammer and/or a masons chisel.

If the doors on the cabinets below the top are glazed with glass you will have to use care to avoid breaking the glass as you bust apart the top. If you can remove the doors beforehand by detaching the hinges it would be a good idea to do that.

The white material used to fasten the top looks like a white silicone material. It is not surprising that you would have some difficulty trying to cut it with a blade pushed into the crack. The rubbery nature of silicone will make it very difficult to cut in this manner.

I do suspect that as you proceed to break up the top that you will get some pieces that are still stuck down by the silicone. A twisting or lever action on the piece will usually make the silicon peel off of one surface or the other. In case it does not want to pull loose you can reach in with a sharp utility knife and cut the silicon easier when it is pulled and stretched by tipping up the top piece.