Do you have other fig plants though? Keep it segregated from them if you do because the mites spread easily, on your hands and clothes even. They are tough to deal with because they are very small and tough to get contact with spray, and their life cycle can be very short in warm weather so contact sprays need to be applied very frequently... Translaminar miticides like spiromesifen are the most effective way to get the job done, and probably the best for something fragile like a green cutting.
If that cutting is still fresh you could try a neem oil extract like Azatrol. *try an experiment at your own risk: recut the bottom of the cutting and put it in an Azatrol solution like a cut flower for a few days.
Whatever you do, you could be a big help to others by reporting if what you try works or doesn't. To actually see these guys you need a handheld microscope, they are cheap and seeing the mites is the quickest way for you to know if a treatment works or not. The only recommendations you will find are for dormant oils and sulfur, since figs are not a major crop there are no pesticides labeled for them.