I have a couple fig cuttings that have FMV. Should I keep those cuttings away from my normal cuttings? How is it transferred? Pruning tools? Air?

Think of it like HIV, it is a blood transfer, so air no, pruning tools yes...unless you live where the mites that spread it you should be able to have them if you want to keep them as long as you take precautions.
I am working on a FMV free orchard since I don't plan (at the moment) to have 100's of trees. I do think malnutrition and other things can look a lot like FMV so I wont be getting rid of anything till I am very sure it is truly and infected tree.

There was an in-depth discussion about FMV last month with some good info and links: http://figs4funforum.websitetoolbox.com/post/fig-mosaic-virus-questions-6556316

How did you know the cuttings were infected--were you told this or did it show on the new leaves? I ask because I've never had fig plants that expressed FMV, although I have tried to focus on heirloom varieties that might have escaped contamination.

I know this because it originated from UC Davis. I am all clear now. I just got to make sure that I wash my tools.

Good answer :)

all fig trees have FMV. knowing this fact, i'm very happy and unconcerned about FMV :) 

I hate to disagree but it is well known that fig trees started from plant tissue cultures which are available from a few locations don't have the virus, it does not carry thru the seeds so if you are lucky enough to get a good tree from a seed then it would not have the virus. Even studies done back in the 1950's list trees that were resistant.  It comes with deformed leaves, deformed fruit and a tree that doesn't grow well.... as I said before I think people misdiagnose plants a lot. There has been a lot of research done and DNA and RNA isolation of the virus, but it is just that a virus not some magical thing that appears in all plants, some get it some don't... the only way to know if your tree has it without obvious signs is a RNA test.... but why would I think I have the flu if I don't have a runny nose or aches and pains and no fever....no sign, no symptoms.... I'd say no virus...