We present the results of CO(J=32)- mapping using the James Clerk Maxwell Telescope of the active star formation region NGC 1333, supplemented by CO(J=10)- mapping from the Onsala Space Observatory millimetre telescope. These maps provide a detailed overview of the complex cluster of overlapping molecular outflows associated with Herbig-Haro (HH) objects and shocked H2, and the far-infrared and submillimetre sources that drive these outflows. We identify about ten molecular outflows and in most cases their driving source. Many of the outflow-driving stars are confirmed or probable Class 0 protostellar objects which drive highly collimated CO jets. We identify HH 12 as the leading bow shock of a large outflow driven by SSV 13B with an orientation close to the plane of the sky. The present rate of energy injection into molecular gas by the outflows, if maintained over a time scale ∼107yr, appears sufficient to disperse the entire NGC 1333 cloud. On the shorter time scale of the current generation of star forming activity (∼105yr), it appears that the star forming core has been broken up by the outflows into a number of low-density shells with star formation activity confined to dense ridges on their periphery.