Hazel, I moved your post from the introductions subforum as it is not an introduction.
Welcome to DIY chatroom.
The answer depends on how well the tiles are stuck down and with what. If it was done right I doubt you'll have any luck saving the tiles. You might get lucky on a few, but granite tiles are relatively thin and since they're rock they definately will crack.
And as thekctermite said, "if it was done right". Who did the job? If it was a DIY job, you can probably get quite a few off as they probably didn't do it correctly. Wrong substrate, wrong adhesive/thinset will increase your chances on saving some. If an adhesive was used, you can try using a heat gun to soften it up. Then take a stiff taping knife and slide under the tile to break the connection by gently lifting while still applying heat. With the larger tiles, you'll need something that will reach deeper into the back to get the penetration you need.
If they used thinset made for granite and a cement backer board as a substrate, you'll be lucky to recover 10% of the tile.