I think, from the sound of your request, that you'd be happier with a centered plant. Centering, however, will not prevent the plant from tilting and perhaps even falling from weight as it grows (a perfectly natural method of self-propagation for Opuntias), it will simply mean that you will have a more aesthetically pleasing looking potted display (in my opinion).
Simply grab some heavy duty leather gloves and gently cradle the plant (around its base) while inverting the pot. Gently tap on the bottom (or have someone else do it), until it all slides out. All this might not even be necessary considering how shallow and unsubstantial the roots of the new plant probably are. You might simply be able to take a trowel around it to a sufficient depth the remove it completely intact. Just be sure to use those gloves!
Carefully break away any excess soil and gently position and replant the cactus into a more desirable pot/location/rotation using, of course, a suitable, quick-draining medium.
Alternatively, leave it as-is. Too much bother to cut, callous and wait yet again for it to establish new roots.