Downhole fluid jet cutting tools having extendible and retractable arms with cutting heads on the ends are disclosed. The jet cutting tools permit casing and other downhole surfaces to be cut utilizing a cutting fluid forced through a jet nozzle assembly. Inflation of an inflatable member within the passageway of the tool moves the jet nozzle assembly when cutting fluid pressure inflates the inflatable member. As a result, a cutting head of the jet nozzle assembly is extended and cutting fluid is forced at high pressure from the passageway to the cutting head where it is expelled through nozzles for cutting casing and the like. The jet cutting tools permit the cutting head to be extended, retracted, and re-extended or redeployed multiple times without the need for being retrieved from the wellbore.