Ideally, if it was a non-lived in structure you'd mechanically remove it but It's nasty and you need the right vacs, ventilation, etc not good to breathe that stuff in. highup is right you can encapsulate the adhesive with a resurfacing material or to remediate it.
First, you can safely seal black mastic and then cover it with paint, epoxy, or their flooring material of choice. Many professional contractors now feel that this is the best solution for dealing with the potentially hazardous material. Black mastic is delicate.