A centering device on a cutting device using an ultrahigh pressure (UHP) hose carrying UHP fluid is designed to be inserted into a pipe or tube and cut the same from the inside out. In one example, the cutting device is for insertion into a wellbore for cutting the casing of the wellbore from within the wellbore with a revolvable UHP hose. The cutting head which effectuates the cut may be centered by the centering device that is generally conical in shape such that a portion of the centering device remains exterior to the pipe or tube as the UHP revolves during the cutting action.