if cheese in fridge starts getting mold,is it safe?
There's no definite answer. Lately (past 5+ years), the USDA has come down hard on mold; not sure what their exact rec is these days, but it errs on the side of tossing it. On the other hand, they didn't used to be so worked up about it, and I and millions of other people routinely cut off mold and eat the rest. On the other hand, since it's already sliced, that introduces the new variably of you not being able to be sure just where what has been growing.
Personally, I'd try it if there are slices that are "mostly" free of visible mold, I'd at least taste one of those. But if it's gotten moldy, it's also been sitting around for a while somewhere, which isn't likely to do much for the flavor - cut cheese doesn't age, it just goes off...
PS: Blue/green/gray is one thing, if you see pink/yellow/black, it'd better be some expensive freaking cheese before I'd play around with it...
PS: It may sound a bit much but I've learned to rinse/wipe off the knife between each cut if I'm actually cutting through a moldy surface/area. Even a trace of mold (or the wrong mold on the wrong cheese) just tastes anywhere from "musty" to outright gross. Which also means you'll know it if it's there whether you can easily see it or not, and for whatever it's worth, I've tasted both many few times and live to write this. :)
this is one of those issues that depends on the type of cheese.
[obviously mold is desirable - and required - for certain types of cheese...roquefort, brie, gorgonzola, camembert...but you already knew that, and those cheeses can obviously also develop undesirable molds as well.]
as for "bad" mold, or anything that indicates spoilage, there are basic rules:
brie, blue, camembert, cottage, neufchatel, feta, ricotta, SLICED or shredded - always need to be tossed once they show any evidence of mold.
american, asiago, baby swiss, jack, mozzarella, muenster, provolone, gorgonzola - safe if you remove the mold; cut at least one inch around the moldy spot.
cheddar, colby, swiss, parmesan, romano, gruyere - same as semisoft.
sooo...had your provolone been in a block, it would have been safe to cut around the mold. but since it was pre-sliced, toss it.