Honed slate tiles with surface scratches
Unfortunately honed slate has a tendency to have light surface scratches if used in the wrong environment, your problem sounds a little more severe, you will get people that say "just re-seal the tiles" & this will make it go away but it does not, it is a quick fix.
You could buy some honing pads to try to hand polish the scratches out but to be honest it is less hassle to probably use the tiles for cuts around the perimeter.
Honed Slate should only really be used in low traffic areas such as bathrooms or walls.
Another solution would be to apply over the light scratches some mineral oil with a small washing sponge as the oil darkens the scratch to the same colour as the slate tile.