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