Please don't try to cut it in half.
It can be done, but should only be attempted by experienced anemone keepers.
They do split, at intervals and under circumstances unclear to anyone. Stress (not life threatening stress) is often cited as stimulating it, but I do not believe this is the only factor. Mine grow like weeds, do not seem stressed in any way I can tell, and went from one to four in less than a year.
Just enjoy it, keep it healthy as you can, and let nature take its course.