Is the concrete/mesh on top of plywood? If so, can you unscrew the plywood from inside the cabinets (if that's how it's attached)? Then you could remove the counter in a single piece.

The mortar bed is a standard practice in a quality installation.
The method you are describing, if you continue, will result in a less than quality finished result.
Direct your attention to just removing the field mosaic tile, leave the mortar bed alone.
After I've chipped out a single tile, I use an old 3/4" wood chisel.

The mortar has to go. The counter I'm replacing this old tile one is single piece laminate. leaving the mortar bed would make the counter too tall (thick).
weedyacres. the mesh is on top of thick wood planking, like 6" wide by 1/2" thick. Not sure how thats attached but I will check that out. I thought maybe trying to remove it all as one piece would be too heavy to maneuver. but it sure beats chipping away at it!

Are you serious, internet dentistry and Forest Gump, at the same time.

just a follow up... the mortar bed was successfully removed. Turned out the easiest method was to ignore the tile top, other that to chip a few away to gain a visual of the wire sticking out at the edges. I found if I hammered at the tile top certain areas would come apart easily, these being the places where the wire mesh was connected. These areas were smooth metal, not mesh, so the mortar came away easily there. At these spots the mesh was nailed onto the wood board beneath. If I aimed my chisel between the wire mesh and the mortar it was relatively easy to separate it in sections. Once the nails were pulled out it was much easier to remove. Once it was all cleared away, all that was left was the wood board. The installer decided to use that board, since it was nice wood and provided a better surface with which to lay the new counter top onto than the "pieces" the counter company provided. Worked out great and the labor it took was worth the savings to us, as we got a price break for saving the installer time.
sorry, snoon....can't make anything out of your comment, though definitely not helpful.

Thanks for the update and the description of how you succeeded!

I'm thinking that leaving the plywood would have made the countertop a bit to high, at least by the thickness of the plywood. Not that it would be an issue to work on, more so that the distance from the top of the drawer to the bottom of the countertop would seem excessive.

I read the first three sentences of this old post and started laughing. Shame on me.