What is solution to discoloring slate?
It looks like that one brick has a lot of iron oxide in it which is leaching into the grout and dripping down. Could be an interesting chromatography experiment.

You will need to remove that brick and examine it to determine the problem. It is also slightly possible there is something behind the brick that is rusting, but that is less likely.

Probably you need to replace that brick and then re-grout the stained areas.