There are two way to do this.

1. The Stockpile Way
   By designating a stockpile right next to your masons workshop, and only allowing the stone you want to use on that stockpile, and removing/forbidding all other stone around the workshop, the mason will grab the stone you want him to use, as that is the closest availble stone.

2. The Fortress Way
   (The name of this way is a reference to "Obsidian Fortress", where only obsidian is being used for the whole fortress.)
   You can simply disallow usage of all other type of stone trough the Z -> Stone Menu.

There are two way to do this.

1. The Stockpile Way
   By designating a stockpile right next to your masons workshop, and only allowing the stone you want to use on that stockpile, and removing/forbidding all other stone around the workshop, the mason will grab the stone you want him to use, as that is the closest availble stone.
   Note that even if you forbid all stones around the workshop, the mason may still gather stones from a z-level below the workshop if they're closer directly. (This has to do with the way the game does pathfinding.) Therefore, it may be a good idea to define a burrow around only the workshop and the stockpile, and restricting your mason to it. Make sure to set the workshop to only be used by the mason you add to the burrow, so you can build another one to make unimportant stuff out of other stones and don't make important stuff out of them. To do this, you may need a manager noble.

2. The Fortress Way
   (The name of this way is a reference to "Obsidian Fortress", where only obsidian is being used for the whole fortress.)
   You can simply disallow usage of all other type of stone trough the Z -> Stone Menu.