Similar to what Ax said, depending on how dirty/contaminated it got, scrub it, soak/rinse and F10 to clean if needed.
I use grape vine in my amazon tree boa enclosures and never had mold issues with it. Perhaps it has to do with what substrate it's kept on? Bark, moss, eco earth may hold humidity and let it wick up into the vine perhaps?
I use it with paper substrates and never get mold. I was having mold issues with those half log hides with bark on them in both ATB and BP caging (with paper substrate) so I got rid of all of those.