I think the pups are actually branches off the main stem, so you would have to cut them free from the main stem. I would take sharp pruners and cut straight across the base of the offset right where it comes off the main stem. Don't pull, cut. The offset on the right (in the first picture) looks like it will come with its own roots (remove carefully) if you go that route, the one on the left may not have any roots. Cuttings should root quickly (within about 3 months starting from a rootless cut, I would expect).
Those pink flowers on your plant are not a match for the CP flowers that I'm familiar with, and the surfaces of the leaves are not spiny on the undersides, unlike the CP I know:
So I would guess you have something different, but very similar-looking.
When you separate the offsets, give them time to heal. Maybe pot them up in dry soil and then wait a week or so to water. If you end up with a rootless cutting, leave it in a place with good ventilation for a couple of days to heal before potting it up. The important thing is not to water immediately after potting up either mother or daughter plants... wait a week or so first.