I am assuming that the cement board is attached to furring strips that is then attached to the concrete basement wall. If the furring is metal, great, if it is wood, ok, but not the best. I just don't like using combustables in situtations like yours. However, if you maintain the proper clearances, (see UL Approved below) it won't be a problem so don't worry about that.
Now, then. Your slate will attach itself just fine to the cement board. I would ask the manufacture's rep where you bought the stove for the proper specs for the grout, just to keep your insurance policy in tact. There is a UL approved assembly that you should follow. If you don't, and burn your house down, you could be in trouble.