Yes you can cut off the babies with their stems and pot up separately in a gritty compost mix in small pots to get them started growing.

Why take them off in the first place. In your first pic. it looks as if the Sempervivum is still in the square pot that you bought it. Just un-pot it and replant in your shallow dish - it does have drainage holes, I hope. The Semp. will keep on producing more and more babies and you will soon have your display.

Bulbaholic. It is actually a bit of plastic liner sticking out from the soil. They are getting a bit crowded in there so thought I'd create some more space.

Moon growe-how gritty should compost be? 50%-50%

That would be about right Amsterdam but, as Bulba says, you can simply plant the whole lot in a shallow dish and let them romp away.

I'm about to set up an alpine/succulent trough and from somewhere (possibly the Alpine Society or similar) I copied the following:
wash compost off roots, re-pot in 50:50 John Innes No2 and grit. Layer of grit in bottom of pot.

Maybe one of the experienced alpine/succulent growers will confirm or otherwise.

Fair enough comment. The reason to wash the roots is that the seller has undoubtedly potted them in a pure peat compost which has minimum drainage. If they are in a soil-based compost then there is no real need to clean the roots.

Thanks for clarifying that, Bulbaholic.