Hmm, I normally use MDF and you can slide a sharp knife carefully under and slice them off - sometimes you get a slice of MDF underneath but that's not usually a problem, just something to raise figure height a little at random when you rebase
The plastic FoW bases have little dips don't they, for the figures to sit in? So sliding anything under and slicing off probably won't work...
Do you ant to re-use the FoW bases? If not then perhaps cut the base apart or chop out round them then carefully slice off the plastic left underneath?
If you want to reuse the bases... I'm a bit stuck...