Well Loyalty, IMHO it looks like you have an esthetic problem. I really understand having a few issues much like yours. Being as this is being posted on a board where anyone can read it, I want to FYI anyone that is new to the hobby or has not done their homework on their reef inhabitants.
True Zoanthus and Palythoa (button polyps) both contain a very dangerous chemical called Palytoxin. This toxin has been documented as one of the most poisonous marine toxins known (Mereish et al, 1991). Palytoxin effects the heart, muscles and nerves causing paralysis and even death. If you have even a small cut or hang nail (usually this salt in the water lets me know very quickly, lol) or if after working on Zoo's, the slightest rub of an itchy eye can have you running to the hospital...I doubt any of our local hospitals would be able to diagnose the problem so make sure (God forbid there is an accident) that the staff is told what you were doing and the name of the toxin.
Most of us that have been doing this for a while (I know I do) research all of our coral for any toxins that can make us sick while propagating and keep a list of which coral and the toxin they hold, just in case.
Ok, now back to your problem, lol! Terry and Dave are correct with cutting the shrooms but I don't believe this would not solve your problem. Mushrooms are technically anemones....they move around if they don't like their placement and the slightest bit left if cut, ripped or otherwise damaged will only cause the shrooms to multiply, that's why they are great for propagation. Unless you literally break the rock with a chisel or dremmil the shrooms out attached to the piece of rock they are on, the slightest piece of shroom left can regrow into a whole new mushroom (or multiples if say two or three small "slime" pieces left grown into new shrooms) so you haven't gotten rid of the problem but have multiplied it.
As far as the zoos, don't worry about hurting them, they can be propagated pretty much the same way so if a cap gets cut, the base will grow a new cap and the cap will grow a new base.
Looking at the pictures you've posted, am I correct that the zoos are low and matted (as opposed to high stems with button polyps)? If they are low and matted, you might want to think about changing their placement to a high flow area...low zoos are naturally found high in the ocean with a lot of surge and even in areas where they are in the surf and left in the air at low tide. Mushrooms seem to like low flow areas. Perhaps by putting this rock in a high flow area, you can direct which way you want the mushrooms to go, they will not like it and move to get to calmer waters. It could take a few months or just a few weeks depends on how fast they want outta there! Not the quickest option but probably the most effective....remember the "saltwater motto"--The only thing made in a hurry is a mess!--but if you do decide to work on removing the mushrooms make sure you take the rock OUT of the tank and work on it in a container of tank water then when finished, move to another container of tank water to dilute any toxins before placing back into your main tank.
Hope this helps give you a few ideas.
Monica
p.s Sorry so long, those that know me know I'm a talker, LOL