I think killing them off while in your tank still might release unwanted waste into the water. I also can not think of anything that would eat them that is reefsafe at the same time.
What I do is take a pair of needlenose pliers, grab ahold of the bass of the mushroom, and I slowly pull them off the rock. If you pull them too fast they could rip, leaving a mess behind, and allowing the parts leftover to regenerate into new mushrooms.
I have learned to grab the base and twist the pliers a few times, wrapping the mushroom around hte pilers, and pull them off slowly. This has always been the best way for me to get rid of the ugly and fast growing mushrooms that compete with my ricordia and zoathids.