^what this guy said..
particularly for SPS, it's a colony of tiny animals..
LPS and softies are a little different depending on the coral.. but same theory.. they are cut differently depending on what they are..
LPS is usually cut with a saw (like a band saw) or seperated between heads if possible
softies can be cut with a knife
SPS is usually cut with some sharp clippers..
most times coral will heal well from being clipped, but sometimes it gets infected and dies. coral has to be able to take a beating, there are fish that pick at it or even eat chunks of it, SPS gets broken off easily (even in the wild).. if coral was that fragile, it wouldn't survive the day to day life in the ocean..