Fluff
Aquarium Advice Addict
You can take a pair of scissors and cut about a 1" thick slice all the way around the rim, then cut that big piece into smaller pieces. The leather will slime up heavily and will look bad for a few days, but will recover.
This is the simplest way to do it and after the coral heals, it will not hurt it as bad aesthetically as just clipping off pieces.
Cutting the rim into one inch pieces works, or you could make your frags larger. I also agree with ziggy to take the coral out of the tank to frag it. I would also have a bucket of water from the tank to put the cut coral into to rinse much of the slime off before returning it to the tank.
Ziggy, that birds nest is really looking great!