People do have great success cutting anemones. I actually want to start to do it. I have read up EXTENSIVELY (probably close to a hundred hours). I have acquired an anemone to start with as well.
While it may work for you, putting them back into a reef is not a good idea. Ideally, anemones should be kept in species tanks with just other fish. Corals and other anemones aren't good for them. After the cut, Allelopathy will irritate the anemone more, they have more of a chance to wander, and if they host clowns, the clowns can irritate them more and cause them to die. While it may be possible to do this. I would not suggest it.
The OP also never stated what kind of anemone he has. What if he has a ritteri? Would you suggest he cut it then? There are certain species that I would not suggest manually trying to propagate (ritteri being one of them). Please don't blindly tell people to cut their anemones and tell them to put them back in their tank. Your first post said to rinse them in the water, which to me means shake them around a bit, then put them back in your tank.