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I trim mine back near where it comes from the plant. After a while it will dry out and you can pull it out with ease. I leave the for a while, mine has pretty white flowers and lots of babies. You can start more plants if you like with the babies.
I trim mine back to the fresh leaf to keep it looking nice. I've had my plant for 25 years, they will make new leaves and old ones will die off but you won't kill your plant by cutting back the tips. I sometimes give mine a haircut when the whole thing gets too crazy, they just keep growing.