I said it's a pain to cut, I didn't say it was hard (still to hard for woodworking tools).
Ever wonder why you go to a stone masons for a head stone and find loads of broken chunks of the stuff in his rack? he hasn't got a clumsy assistant that's for sure.
Much like wood it can have faults and stresses internally, especially a mottled marble as is being described by the OP. A wet saw helps with limiting the amount of force on the cut and clears the chips away to reduce heat build up, all of which are great ways to overstress and encourage a flaw to do more than a little ping. (wet cutting also keeps the silicates out the air, but have a *** while your doing it to filter it out and you'll be right)
based on the size of the slab, I'd say it's a fairly big chance it's got some flaws in it, you could easierly ruin the entire thing if you hit one dry, you also need to support the cut on both sides for the entire cut.
now, as it's effectively going scrap, no reason not to have a go, the edges can be polished with wet diamond pads (can be got for cheap for grinders), working your way down the grades as you would anything else. mark a line straight across thats about the depth of your grinder head away from where you want the cut, support the slab off the ground as close to where the cut is as possible and every 12 inchs out to the end, clamp a straight piece of wood to your line and run your grinders back edge against it, so you only have to concentrate on keeping it going in a straight line. multiple passes is better than 1 big cut and will be less likely to overheat the blade or crack the slab. if you can get a bit of water on the cut (a spray bottle) then go for it, in moderation as you are using a power tool here (bzzzz). it's going to be messy, so don't wear you wifes best dress and do it outside.
make yourself a sharpening station then a few worktop protectors (not chopping boards, please not chopping boards) as mentioned and maybe take a small chunk and polish it in to a pendent for the wife so she gets something out of it.