Last time I worked with slate here in the U.S., I rented a tile saw (water cooled) from my favorite DIY store for about $40 a day. It works well with slate and only took a few hours for the entire job. Slate is soft and easily cut...
It depends what it's for Robo. It's usual to cut roof slates with a slating axe or even one of those little firewood choppers. You turn the slate upside down to cut it, and it gives you the proper "riven" edge on the face side.
Otherwise, for a smooth cut, use what the others have suggested.