A cutting head assembly uses multiple cutting heads directing ultra-high pressure fluid in different directions towards an inner surface of a pipe to be cut in order to complete a full cut of the pipe while rotating or revolving the multiple cutting heads less than 360 degrees relative to central axis. The ultra-high pressure fluid mixes with abrasive inside fittings on or near each of the nozzles to further assist with cutting through the pipe. Some cutting head assemblies have two nozzles, while other cutting head assemblies have three or four nozzles.