Be very careful what you use on marble; many cleaning products can permanently etch the surface. Shaklee Basic H2 all purpose cleaner will remove it safely. Do a search on the web and you'll find a distributor.

I have a famous and tedious answer that might or might not work....whenever I have to remove something like that I use a very high quality chisel and slide it over the surface. On a good quality tile, it will (if carefully done) slip under the contact cement and cut it from the base. It might or might not work, but I wanted to share that option. I've used this trick for grout, glues, etc., and so far, so good...and not ruined the surface but you have to remember to be careful to keep the blade flat on the surface you want, and slowly try to push it under without digging in.

There are a few solvents available like "goof off" that I have found very good at removing adhesives. They can be sprayed on and worked with a stiff brush on concrete or You might want to try a portable electric-powered concrete planer with an attached dust bag. It works well for leveling and finishing rough concrete floors. I think it can easily chew on the thinset mortar. Not totally dust-free operation but much less dust spread than using grinding wheels. Ciciliot

In some older applications, a black colored adhesive (called "cutback adhesive") was used to hold vinyl tiles. Both the tiles and the adhesive could contain asbestos. If you have old vinyl tiles or the adhesive residue on your concrete floor is black, you are much better off simply covering it with your new flooring. If that's not possible, hire a flooring specialist properly trained in dealing with asbestos to remove the adhesive. Your family's health is worth the cost.