Slash and burn, baby! They are resilient. If you don't care about "preserving" the mother colony (i.e. it's not your central showpiece) you can just snip off pieces of the disk with scissors, then mount them with your favorite method. An average-sized disk might be able to yield 6 or 8 frags.
Once you have the pieces, dip/rinse in fresh tank water, then mount. You can mount using the lazy method (put them in a big cup with live rock rubble in the bottom and wait for them to attach) or more proactive methods - for instance, tie them to live rock with bits of netting or zipties.
If you care about preserving the parent colony, you might want to just take one or two frags at a time. Or, keep an eye on the stalk - they will often form tiny little buds off to the side that you can snip off and mount.