How to make a personalized stone cutter

It would be much easier to just add your stone recipes to the existing stonecutter; you can literally just add custom stonecutter recipes without any hassle.

If you want to make a custom stone cutter, it's going to be a bit more convoluted. You'll need to make a custom block model if you want it to look like the vanilla stonecutter, (Using blockbench or something), with an animated texture, (for the sawblade.) You'll then need to make a custom GUI that opens when the block is right-clicked.

The trouble with the Stonecutter is that its crafting mechanics are WAY more complicated than the Vanilla crafting table, at least in terms of the GUI. The easiest way to do this would be to simply have an input slot for your stone material, and then multiple output slots for each variant, which clear the other output slots when an item is removed from them.

However, if you REALLY need a custom stonecutter identical to the vanilla one for some reason; it's still possible, it'll just take a lot of effort. You'll need to copy the Vanilla GUI, (which you can find in your game files, or using a tool like MC Assets), then make a seperate button graphic for every single crafting recipe. (You'll also need some way to get isometric renders of each block, which I'm not entirely sure how to do.) You'll have to build your custom GUI using basic text buttons that have display conditions based on the input crafting material; and that determine the item in the output slot when pressed. Then, you'll need to lock the GUI code and replace your text buttons with the loads and loads of custom images you made for each crafting recipe, which is an entirely different tutorial. 

...Again, technically possible, but will probably take at least a week or two to get working. Unless you absolutely need a custom crafting station, I recommend using the vanilla one.