I am not sure you need a new tyre, but it is hard to see from your photos. Does that cut go all the way through or is it just a cut?
Tyres get cut up all the time (especially if you love somewhere flinty) - as long as it doesn't go all the way through the canvas, then usually it isn't an issue. Some people glue the cuts, I don't bother. Even if it goes all the way through, a boot will fix most tiny cuts like that.