[Racinmason]

A tile saw would be ideal. If that's not available, Chandler's idea will work. I've always had great luck using a standard power saw with a dry diamond blade. I just seem to have more control with that saw because it's much easier to hold onto. You will be shocked at how easy that stone cuts. I've even used a sawzall with a wood blade before to cut that lightweight stone.
You probably want to keep a gap between the stone and the threshold, that stone will have a tendency to pock off if there's much weight placed on it. I would also keep it off of the concrete floor.

 

[Racinmason]

I did my fire place with a product similar. I bought a HF diamond wet saw and learn quickly my stone product was HARD. It took a while for the diamond blade to eat its way through each cut. Thankfully this product is not very thick.

I would be very nervous about this product glued/a fixed to the bottom of a door way. The door closing causing vibrations and freezing temps.

Was your stone actual thin stone veneer or cultured stone made of lightweight concrete? I've never had any problems cutting this stuff. I've even used a handsaw once. It scores easily with a razor knife. Maybe it was your blade?

 

[Racinmason]

The stuff I used was rock and hard. The only part of this that was man made was the fact someone took small pieces and created sheets for easy assembly for the DIY crowd. I liked it on the inside because the cracks between the stones did not have to be grouted and if you were careful the sheets did not need anything either.

I did one fireplace long ago with the fake bricks and had to grout it all in which was a lot of work for me.

The real stuff does have that "real" look, even up close. I do like the dry stack look, especially when the joints are tight.
Some of that stone is incredibly hard to cut.

 

[Racinmason]

I believe he has to split a piece lengthways. Those cutoff pieces don't even need to be cut all the way through, 2/3 of the way through with a chop saw then break it by hand, they're very brittle. Don't drop a piece!