It works well but can have some issues.
With a nice centrifuge (Omega)_ juicer:
You will want to remove the outer layer of skin, the waxy paper like stuff
you will want to remove the vascular core tissue
you will want to use hydrated cuttings
you will want to use extra water to wash out the mash
you can get a lot of foam, but a quick rinse of that works well
you can't do that much at once and smaller batches are more efficient than larger ones
done with a fresh cutting it works well, the pulp having hardly any bitterness and the juice being very bitter, you can take shots of the juice
If you look close it is not so much juice as a liquid with a lot of cellular matter in it, if you dry the juice you will notice this more and if you let it settle the cloudiness goes away and becomes a sediment layer
it is wise to note that candicine can be found in some of these cacti and while it is unlikely to found in a tea or a crystal extract of alkaloids it is more likely to be ingested with juice and may be undesirable.
Secondly reports of persistent adverse effects have been known from some clones when consumed raw, this is not well understood but it might not be wise to ingest raw cactus, or at least it might lead to greater risk of negative side effects.
I am not sure how trapped the mescaline is, I believe it is found in rather soluble salts. Perhaps I am wrong.