Small squares as pixels would be time consuming, but would allow high detail even without a CNC.

Drag knife on a cricut wouldn't be strong enough for thick tile.Mill with a O-flute single flute plastic routing bit would be the way to go. 1/8" diameter, carbide, as fast the spindle will turn. Flute length as short as the tile thickness will allow. You'd want a few spares, you'll probably break a couple getting it tweaked. Start at .030 chip load, full width and depth, probably don't need a finish pass as the edge roughness will increase adhesion and won't be visible. Don't use coolant, don't breathe the dust, wear a P99 or P100 respirator, shop vac with HEPA for cleanup. Some tile may have abrasive fiber in it and will shorten tool life.

For fixturing, I think I'd use strap clamps and bars around edges. Use tabs between pieces almost like a stencil, lot of CAM software has a setting for auto tabs on profile cuts, cut from center to edges. Vacuum tables can be real temperamental, slow way down and still tab if trying to hold with vacuum. Double sided carpet tape can do it but has to be removed with acetone and IDK if that would effect the tile.

Just spitballing, I'd be afraid metal mesh might cause de-adherence over time, especially if it corordes. I really like the mesh idea. Loose cotton fabric like cheese cloth or maybe a little tougher would absorb the tar and might make it even stronger, just have to pour at a high enough temp. Fiberglass sheet might also work.