What should one cut rockwool with? (specifically Rockmur Kraft)

Hand saw or large knife, possibly guillotine if you have one. Less nasty than PIR for dust but harder to get a straight edge.

Keep the roll tightly wound, preferably in its shrink-wrap covering and use a handsaw.

I can't really say about the dust, it never seems to bother me

Thanks. A knife sounds good from the point of view of not producing too much dust. Does it need a serrated edge or is just plain sharp OK?

It's not a roll, it's panels:-

OK, I'm not particularly susceptible to dust etc. so that sounds as if it should be ok.

still use a handsaw, I used one for some of their acoustic slabs

I have used this for cutting PIR, it does say it is suitable for mineral too

I've used one of those - pretty good but there's knack to it I've not quite mastered. Up to 50mm I still find deep score/snap (like plasterboard) works best for PIR. Not sure about the OP's slabs - I'd guess wood saw.

And really, use a decent dust mask. While the dust might not irritate short term you've no idea what lingering fibres might do.

For PIR I use a serrated knife, which I think should work here. I bought a pack of cheap 'steak knives' on Amazon which do the job, but a bread knife would probably work too and have a longer reach. The main thing is to have a thin serrated blade - some knives have quite a thick blade and are more work as a result, although probably not such a problem on wool which has more give than PIR. (thin knives are also better at cutting bread, which I'd guess has similar consistency as these wool slabs)

For actual sheep's wool, I use scissors.

Theo

I ran an angle grinder down either side of a worn wood cutting saw. You need a blade length significantly longer than the roll width.

I use wallpaper scissors to cut the floppy rockwool, and a stanley knife to cut the hard compressed rockwool batts that Wickes used to sell for sound-proofing purposes (but they don't seem to stock it now).

Even the floppy stuff can be cut with stanley knife. Just compress it flat on a hard surface with a length of 4x1 or similar and cut along the wood edge.

Wear a mask, some sort of gloves, and overalls. Fibreglass can leave you feeling quite hitchy, if it gets to the skin.

I ended up with a bloody great pus filled swelling on the side of my neck the size of a pigeon egg.

That was in Johannesburg, though.

Lanced washed daily and fed on antibiotics for 10 days.

I hate the stuff with a passion.

Full marks for mentioning an angle grinder! This has been sadly lacking around here for some time.

A really sharp bread knife with at least an 8" blade, serrated or plain. Or perhaps a pair of really sharp garden shears?

I've never encountered those, ever