Unearthing the fossilized bones of dinosaurs without destroying them is already a pretty fiddly process, one that requires time, patience, and many, many delicate brushes. But when you're talking not about bones but the even more delicate tracks that dinosaurs left behind, the process gets that much trickier.
In response to reading about some ancient marble-cutting techniques, commenter and ichnologist Phaton explained that there were some remarkable similarities between the techniques of old stone-cutters and modern methods of dino-track salvage:
I had to figure out a way to remove a bunch of rock from a specimen with out damaging the fossil footprint. We were in the process of moving to a new building with a weight restriction on the floor and the block was going to probably be too heavy. The footprint, while large (tyranosaurid), was quite fragile so power tools were out of the question. In trying to figure something out I looked into a lot of ancient techniques. What I ended up using was a modification on a Chinese bow saw
but instead of coiling bronze wire between the bow I coiled it around an iron shaft so that it was a one man operation... I don't remember why but I think I called it a Phoenician saw for some reason (a google search turns up nothing useful). Anyways to make a long story shortish: the key to ancient rock cutting it time. As long as you have an abrasive harder then what you are cutting you are going to succeed eventually. Though I didn't actually succeed myself because before I could really start cutting we found really small turtle tracks associated with the theropod track and ended up needing to keep the whole block(it was one of those things where the theropod track was so imposing that you just didn't notice the smaller prints... but once you saw one...).
Top image: Greg Willis