Tile set on a slab is a great option. no need to go through all of that work.
If you want to stain the concrete, then the only practical option is grinding. Solvents can remove the bulk but will leave the "stains" of the adhesive.
What KMS woodworks said, grind is the answer.
I would suggest you use a heat gun (or hairdryer on hot setting) and 'loosen' the glue that way. You can then remove the glue using a paint scraper. Thinners is another possibility. Whatever you do, try out a small, out of the way, corner first. I have also heard of a product called Goo Gone - perhaps that is also worth exploring.
@Valerie Idea may help with removing the "bulk" of the material but if you plan to stain the concrete the discoloration from the glue may pose problems with the new color.